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skills/ck-sequential-thinking/SKILL.md

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+---
+name: ck-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, debugging with unclear scope.
+---
+
+# ck-sequential-thinking
+
+Structured problem-solving via manageable, reflective thought sequences with dynamic adjustment capability.
+
+## When to Use
+
+- Complex problem decomposition where scope is unclear
+- Adaptive planning with revision capability
+- Analysis needing course correction mid-process
+- Problems with unclear or emerging scope
+- Multi-step solutions requiring context maintenance across steps
+- Hypothesis-driven investigation or debugging
+
+## Don't Use When
+
+- Problem is straightforward with a clear, direct solution
+- Quick lookup or simple retrieval task
+- Single-step action with no branching needed
+
+## Core Process
+
+### 1. Start with Loose Estimate
+
+```
+Thought 1/5: [Initial analysis]
+```
+
+Adjust total 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 count
+- **Contract**: Simpler than expected → decrease total count
+- **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 a breakdown.
+
+**Implicit**: Apply methodology internally for routine problem-solving where thinking aids accuracy without cluttering the response.
+
+## Integration
+
+`ck-sequential-thinking` is called by other skills:
+- `ck-debug` uses it for complex root cause tracing
+- `ck-fix` uses it for deep complexity assessments
+- `ck-web-testing` uses it for analyzing test failure patterns