### Install Sequential Thinking Skill

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/README.md

Instructions for adding the sequential-thinking-skill to your Claude Code environment, either via a direct URL or manual cloning.

```bash
npx skills add https://github.com/thedotmack/sequential-thinking-skill --skill sequential-thinking
```

```bash
git clone https://github.com/thedotmack/sequential-thinking-skill.git
cp -r sequential-thinking-skill/sequential-thinking ~/.claude/skills/
```

--------------------------------

### Example Sequential Thinking Output

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/README.md

Demonstrates the formatted output and status lines generated during sequential thinking processes, including thoughts, revisions, and branches.

```text
💭 Thought 1/5
First, I need to clarify what type of auction we're dealing with.
I'll assume sealed-bid first-price unless told otherwise.
[1/5] history=1 next=true

🔄 Revision 3/5 (revising thought 1)
Wait — I assumed one format, but the question is generic.
I should cover multiple auction types. Changing approach.
[3/5] history=3 next=true

🌿 Branch 4/7 (from thought 2, ID: vickrey)
In a Vickrey auction, the dominant strategy is to bid your true
valuation regardless of the number of players. Exploring this path.
[4/7] history=4 branches=vickrey next=true
```

--------------------------------

### Example Thought Output with Status Line

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/README.md

Illustrates the combined output of a thought header and content to stderr, followed by a compact status line to stdout, as generated by the skill.

```text
💭 Thought 4/7
In a Vickrey auction, the dominant strategy is...
[4/7] history=4 branches=vickrey,english next=true
```

--------------------------------

### Reset Sequential Thinking State

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Required before starting any new thinking session to clear previous state. Run via `bun`.

```bash
bun scripts/think.ts --reset
```

--------------------------------

### Reset State

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Resets the state of the sequential thinking session. This command must be run before starting any new thinking session.

```APIDOC
## Reset (required before every new session)

```bash
bun scripts/think.ts --reset
```
```

--------------------------------

### Project Structure Overview

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/README.md

This snippet displays the directory structure of the sequential-thinking-skill project. It shows the main skill logic in `sequential-thinking/scripts/think.ts` and supporting files.

```tree
sequential-thinking-skill/
├── sequential-thinking/
│   ├── SKILL.md                       # Skill definition and protocol
│   ├── scripts/
│   │   └── think.ts                   # TypeScript state machine
│   └── references/
│       └── example-session.md         # Worked example with all features
├── README.md
├── LICENSE
└── .gitignore
```

--------------------------------

### Sequential Thinking Skill Commands

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/README.md

Lists the available CLI commands for interacting with the sequential-thinking-skill, including options for resetting state, submitting thoughts, marking revisions, branching, and checking status.

```bash
--reset
```

```bash
--thought "..." --thoughtNumber N --totalThoughts M --nextThoughtNeeded true/false
```

```bash
--isRevision --revisesThought N
```

```bash
--branchFromThought N --branchId "label"
```

```bash
--needsMoreThoughts
```

```bash
--status
```

--------------------------------

### Inspect Full Sequential Thinking State

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Retrieves the complete history of thoughts and branch details. Returns output in JSON format.

```bash
bun scripts/think.ts --status
```

--------------------------------

### Hypothesis Generation on Optimal Strategies

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/references/example-session.md

This thought generates a hypothesis summarizing the optimal strategies for different auction formats based on the analysis, proposing to verify it against the revenue equivalence theorem.

```text
💭 Thought 6/7
Hypothesis: The optimal strategy depends entirely on auction format.
For 3 players: First-price sealed → bid 2/3 of value.
Vickrey/English → bid true value. Dutch → equivalent to first-price.
Let me verify this against the revenue equivalence theorem before
concluding.
[6/7] history=6 branches=vickrey,english next=true
```

--------------------------------

### Verification and Final Answer

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/references/example-session.md

This final thought verifies the hypothesis using the revenue equivalence theorem, confirming the optimal strategies for first-price/Dutch and second-price/English auctions for n players.

```text
💭 Thought 7/7
Verification: Revenue equivalence theorem confirms all four standard
auction formats yield the same expected revenue under symmetric
independent private values. The strategies:

• First-price sealed / Dutch: bid (n-1)/n × value = 2/3v
• Second-price sealed / English: bid true value = v

Both are equilibrium strategies. The 3-player case doesn't introduce
special considerations beyond the general n-player formulas.
Final answer confirmed.
[7/7] history=7 branches=vickrey,english next=false
```

--------------------------------

### Submit a Branch

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Explores an alternative path or hypothesis from a prior thought. This allows for parallel reasoning or exploring different solutions.

```APIDOC
## Submit a Branch

Explores an alternative path from a prior thought. Requires both `--branchFromThought` and `--branchId`.

```bash
bun scripts/think.ts \
  --thought "Alternative approach" \
  --thoughtNumber 4 \
  --totalThoughts 7 \
  --nextThoughtNeeded true \
  --branchFromThought 2 --branchId alt-approach
```
```

--------------------------------

### Sealed-Bid First-Price Auction Analysis

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/references/example-session.md

This thought analyzes the symmetric Bayesian Nash equilibrium bidding strategy for a 3-player, sealed-bid first-price auction with uniformly distributed private values.

```text
💭 Thought 2/5
In a sealed-bid first-price auction with 3 players and independent
private values uniformly distributed on [0,1], the symmetric Bayesian
Nash equilibrium bidding strategy is b(v) = v * (n-1)/n = v * 2/3.
Each player shades their bid below their true valuation.
[2/5] history=2 next=true
```

--------------------------------

### Submit a Branch from a Thought

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Explores an alternative path from a previously submitted thought. Requires `--branchFromThought` and `--branchId` flags to specify the origin and label of the branch.

```bash
bun scripts/think.ts \
  --thought "Alternative approach" \
  --thoughtNumber 4 \
  --totalThoughts 7 \
  --nextThoughtNeeded true \
  --branchFromThought 2 --branchId alt-approach
```

--------------------------------

### Inspect Full State

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Retrieves the complete history of thoughts, including any revisions and branch details, for the current session.

```APIDOC
## Inspect Full State

```bash
bun scripts/think.ts --status
```

Returns JSON with `fullHistory` and `branchDetails`.
```

--------------------------------

### Submit a Sequential Thought

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Submits a single step of analysis. Ensure `thoughtNumber` is incremented for each new thought. `nextThoughtNeeded` should be `true` to continue the sequence.

```bash
bun scripts/think.ts \
  --thought "Your analysis for this step" \
  --thoughtNumber 1 \
  --totalThoughts 5 \
  --nextThoughtNeeded true
```

--------------------------------

### Initial Auction Type Framing

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/references/example-session.md

This thought process clarifies the need to define the auction type, considering common formats like English, Dutch, and sealed-bid auctions, before proceeding with analysis.

```text
💭 Thought 1/5
First, I need to clarify what type of auction we're dealing with.
Common types: English (ascending), Dutch (descending), sealed-bid
first-price, sealed-bid second-price (Vickrey). The optimal strategy
differs significantly by type. I'll assume a sealed-bid first-price
auction unless told otherwise.
[1/5] history=1 next=true
```

--------------------------------

### English Auction Dominant Strategy

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/references/example-session.md

This thought analyzes the dominant strategy for an English (ascending) auction, which is to bid until the price reaches one's valuation, making it strategically equivalent to the Vickrey auction.

```text
🌿 Branch 5/7 (from thought 2, ID: english)
In an English (ascending) auction with 3 players, the dominant
strategy is to stay in the bidding until the price reaches your
valuation, then drop out. The winner is the last remaining bidder,
paying just above the second-highest valuation. Strategically
equivalent to the Vickrey auction.
[5/7] history=5 branches=vickrey,english next=true
```

--------------------------------

### Submit a Thought

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Submits a single thought or analysis step in the sequential thinking process. This is the primary method for advancing the reasoning chain.

```APIDOC
## Submit a Thought

Required flags: `--thought`, `--thoughtNumber`, `--totalThoughts`, `--nextThoughtNeeded`

```bash
bun scripts/think.ts \
  --thought "Your analysis for this step" \
  --thoughtNumber 1 \
  --totalThoughts 5 \
  --nextThoughtNeeded true
```
```

--------------------------------

### Submit a Revision to a Thought

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Corrects or modifies a previous thought. The original thought remains in history, and the revision is added as a new entry. Requires `--isRevision` and `--revisesThought` flags.

```bash
bun scripts/think.ts \
  --thought "Corrected analysis" \
  --thoughtNumber 3 \
  --totalThoughts 5 \
  --nextThoughtNeeded true \
  --isRevision --revisesThought 1
```

--------------------------------

### Revision of Initial Assumption

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/references/example-session.md

This thought revises the initial assumption about the auction type, recognizing the need to address multiple formats due to the generic nature of the question.

```text
🔄 Revision 3/5 (revising thought 1)
Wait — I assumed sealed-bid first-price, but the question says
"auction" generically. I should cover the dominant strategy for
the most common types rather than assuming one. This changes my
approach: I need to address multiple formats.
[3/5] history=3 next=true
```

--------------------------------

### Signal Need for More Thoughts

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Indicates that the estimated `totalThoughts` is insufficient and more steps are required. Use when the scope of the problem is larger than initially anticipated.

```bash
bun scripts/think.ts \
  --thought "Scope is larger than expected" \
  --thoughtNumber 6 \
  --totalThoughts 8 \
  --nextThoughtNeeded true \
  --needsMoreThoughts
```

--------------------------------

### Vickrey Auction Dominant Strategy

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/references/example-session.md

This thought explores the dominant strategy for a Vickrey (second-price sealed-bid) auction, where bidding the true valuation is optimal regardless of the number of players.

```text
🌿 Branch 4/7 (from thought 2, ID: vickrey)
In a Vickrey (second-price sealed-bid) auction, the dominant strategy
is to bid your true valuation regardless of the number of players.
With 3 players, each bids v. The winner pays the second-highest bid.
This is strategy-proof: no player benefits from deviating.
[4/7] history=4 branches=vickrey next=true
```

--------------------------------

### Submit a Revision

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Revises a previous thought. The original thought remains in the history, and the revision is appended as a new entry. Use this to correct or update prior analysis.

```APIDOC
## Submit a Revision

Revises a previous thought. The original stays in history; the revision is appended as a new entry. Requires `--isRevision` and `--revisesThought`.

```bash
bun scripts/think.ts \
  --thought "Corrected analysis" \
  --thoughtNumber 3 \
  --totalThoughts 5 \
  --nextThoughtNeeded true \
  --isRevision --revisesThought 1
```
```

--------------------------------

### Extend Depth

Source: https://github.com/thedotmack/sequential-thinking-skill/blob/main/sequential-thinking/SKILL.md

Signals that the problem requires more thoughts than initially estimated. This dynamically adjusts the expected `totalThoughts`.

```APIDOC
## Extend Depth

Signal that more thoughts are needed beyond the original estimate.

```bash
bun scripts/think.ts \
  --thought "Scope is larger than expected" \
  --thoughtNumber 6 \
  --totalThoughts 8 \
  --nextThoughtNeeded true \
  --needsMoreThoughts
```
```

=== COMPLETE CONTENT === This response contains all available snippets from this library. No additional content exists. Do not make further requests.