ak-sequential-thinking

name	ak:sequential-thinking
description	Apply step-by-step analysis for complex problems with revision capability. Use for multi-step reasoning, hypothesis verification, adaptive planning, problem decomposition, course correction.
user-invocable	true
when_to_use	Invoke for multi-step reasoning with revisions.
category	utilities
keywords	["reasoning","step-by-step","analysis"]
license	MIT
argument-hint	[problem to analyze step-by-step]
metadata	{"author":"agentkit","version":"1.0.0"}

Sequential Thinking

Structured problem-solving via manageable, reflective thought sequences with dynamic adjustment.

When to Apply

• Complex problem decomposition
• Adaptive planning with revision capability
• Analysis needing course correction
• Problems with unclear/emerging scope
• Multi-step solutions requiring context maintenance
• Hypothesis-driven investigation/debugging

Core Process

1. Start with Loose Estimate

Thought 1/5: [Initial analysis]

Adjust dynamically as understanding evolves.

2. Structure Each Thought

• Build on previous context explicitly
• Address one aspect per thought
• State assumptions, uncertainties, realizations
• Signal what next thought should address

3. Apply Dynamic Adjustment

• Expand: More complexity discovered → increase total
• Contract: Simpler than expected → decrease total
• Revise: New insight invalidates previous → mark revision
• Branch: Multiple approaches → explore alternatives

4. Use Revision When Needed

Thought 5/8 [REVISION of Thought 2]: [Corrected understanding]
- Original: [What was stated]
- Why revised: [New insight]
- Impact: [What changes]

5. Branch for Alternatives

Thought 4/7 [BRANCH A from Thought 2]: [Approach A]
Thought 4/7 [BRANCH B from Thought 2]: [Approach B]

Compare explicitly, converge with decision rationale.

6. Generate & Verify Hypotheses

Thought 6/9 [HYPOTHESIS]: [Proposed solution]
Thought 7/9 [VERIFICATION]: [Test results]

Iterate until hypothesis verified.

7. Complete Only When Ready

Mark final: Thought N/N [FINAL]

Complete when:

• Solution verified
• All critical aspects addressed
• Confidence achieved
• No outstanding uncertainties

Application Modes

Explicit: Use visible thought markers when complexity warrants visible reasoning or user requests breakdown.

Implicit: Apply methodology internally for routine problem-solving where thinking aids accuracy without cluttering response.

Scripts (Optional)

Optional scripts for deterministic validation/tracking:

• scripts/process-thought.js - Validate & track thoughts with history
• scripts/format-thought.js - Format for display (box/markdown/simple)

See README.md for usage examples. Use when validation/persistence needed; otherwise apply methodology directly.

References

Load when deeper understanding needed:

• references/core-patterns.md - Revision & branching patterns
• references/examples-api.md - API design example
• references/examples-debug.md - Debugging example
• references/examples-architecture.md - Architecture decision example
• references/advanced-techniques.md - Spiral refinement, hypothesis testing, convergence
• references/advanced-strategies.md - Uncertainty, revision cascades, meta-thinking