integrated-reasoning（综合推理）

Integrated Reasoning - Meta-Orchestration Guide

Purpose: Guide for selecting and orchestrating the optimal reasoning methodology for your problem. Analyzes problem characteristics and recommends tree-of-thoughts, breadth-of-thought, self-reflecting-chain, or direct analysis.

When to Use Integrated Reasoning

✅ Use when:

• Facing complex problem, unsure which reasoning approach to use
• Problem has 8+ decision dimensions (architectural decision, strategic planning)
• Need >90% confidence in solution
• High-stakes decision with long-term implications
• Problem spans multiple domains (technical + business + organizational)

❌ Don't use when:

• Problem clearly fits one pattern (use that pattern directly)
• Simple decision with obvious answer
• Time-critical with straightforward trade-offs

Reasoning Pattern Selection Guide

Decision Tree: Which Pattern to Use?

Question 1: Does problem require sequential reasoning?

• ✅ Yes (steps have dependencies) → Self-Reflecting Chain

- Examples: Debugging, mathematical proofs, causal analysis - Go to Section: Self-Reflecting Chain

• ❌ No (steps are independent) → Continue to Question 2

Question 2: Are evaluation criteria clear?

• ✅ Yes (can score/rank solutions) → Tree of Thoughts

- Examples: Optimization problems, architectural choices with metrics - Go to Section: Tree of Thoughts

• ❌ No (unclear how to evaluate) → Continue to Question 3

Question 3: Is solution space unknown?

• ✅ Yes (don't know all options) → Breadth of Thought

- Examples: Novel problems, comprehensive planning, debugging complex issues - Go to Section: Breadth of Thought

• ❌ No (solution space known) → Direct Analysis

- No special reasoning pattern needed - Apply standard analytical thinking

Pattern Comparison Matrix

Section: Tree of Thoughts

Use when:

• Problem has multiple viable solution approaches (3+)
• Can define clear evaluation criteria
• Need to find THE optimal solution (not just any solution)
• Trade-offs exist between competing approaches
• Strategic decisions with long-term impact

Methodology:

1. Decompose into 5+ distinct approaches
2. Explore each branch with self-reflection
3. Evaluate rigorously (5 criteria: Novelty, Feasibility, Completeness, Confidence, Alignment)
4. Select best branch, recurse 4-6 levels deep
5. Return optimal solution with 80-95% confidence

Load skill: tree-of-thoughts

Examples:

• "Choose API architecture: REST, GraphQL, gRPC, or WebSocket?"
• "Design caching strategy balancing latency, consistency, and cost"
• "Select database: SQL, NoSQL, NewSQL, or Time-Series?"

Section: Breadth of Thought

Use when:

• Solution space is unknown or unexplored
• Need multiple viable options (3-5), not just one best
• Can't afford to miss viable alternatives
• Novel/unprecedented problem
• Debugging with multiple potential causes
• High-stakes where premature convergence is risky

Methodology:

1. Map solution space: 8-10 fundamentally distinct approaches
2. Explore each approach thoroughly
3. Prune conservatively (only remove <40% confidence)
4. Expand survivors into 5 sub-approaches each
5. Return top 3-5 solutions with trade-off analysis

Load skill: breadth-of-thought

Examples:

• "Redesign data pipeline - batch, streaming, hybrid, or other?"
• "System crashes intermittently - network, DB, memory, race, config?"
• "Comprehensive feature planning with multiple implementation strategies"

Section: Self-Reflecting Chain

Use when:

• Steps have sequential dependencies
• Logical reasoning required (deductive, causal, mathematical)
• Need to trace exact reasoning path
• Error detection and correction critical
• Debugging (trace bug through execution flow)
• Sequential planning where order matters

Methodology:

1. Decompose into sequential steps
2. Execute each step with deep self-reflection
3. Validate logic at each step (confidence ≥70%)
4. Backtrack when errors detected or confidence low (<60%)
5. Return conclusion with full reasoning trace

Load skill: self-reflecting-chain

Examples:

• "Debug this race condition by tracing execution step-by-step"
• "Prove this mathematical theorem with logical steps"
• "Plan project where each phase depends on previous completion"

Section: Direct Analysis

Use when:

• Problem is straightforward with clear solution
• Time-critical decision with simple trade-offs
• Solution space has 1-2 obvious options
• No special reasoning pattern needed

Methodology:

1. Analyze problem directly
2. Consider 1-2 obvious alternatives
3. Make decision based on clear criteria
4. Document briefly

No skill needed - use standard analytical thinking

Examples:

• "Fix this syntax error"
• "Choose between two similar libraries with clear documentation"
• "Schedule meeting for team of 5"

Orchestration: Combining Multiple Patterns

Complex problems may need multiple patterns:

Pattern 1: Sequential Orchestration

When: Problem has multiple phases with different reasoning needs

Example: System architecture redesign

1. Phase 1: Use Breadth of Thought to explore all architectural options (10 options)
2. Phase 2: Use Tree of Thoughts to find optimal within top 3 categories
3. Phase 3: Use Self-Reflecting Chain to validate migration path step-by-step

Pattern 2: Parallel Comparison

When: Need to compare multiple reasoning approaches

Example: Critical business decision

1. Branch A: Apply Tree of Thoughts assuming clear criteria
2. Branch B: Apply Breadth of Thought exploring unknown alternatives
3. Compare: Which approach gave higher confidence?
4. Use: Solution from higher-confidence approach

Confidence Calibration

Expected confidence by pattern:

• Tree of Thoughts: 80-95% (deep exploration of best path)
• Breadth of Thought: 70-85% (wide coverage, less depth)
• Self-Reflecting Chain: 70-90% (depends on weakest link in chain)
• Direct Analysis: 60-80% (quick analysis, less rigor)

Confidence thresholds:

• 90-95%: Exceptional evidence, suitable for critical decisions
• 80-89%: High confidence, suitable for important decisions
• 70-79%: Medium confidence, consider additional validation
• 60-69%: Low confidence, recommend further investigation
• <60%: Very low confidence, gather more information

Quick Reference: Choose Your Pattern

START
  │
  ├─ Sequential dependencies? → YES → Self-Reflecting Chain
  │                             NO ↓
  ├─ Clear evaluation criteria? → YES → Tree of Thoughts
  │                               NO ↓
  ├─ Solution space unknown? → YES → Breadth of Thought
  │                           NO ↓
  └─ Simple/obvious solution → Direct Analysis

Meta-Analysis Checklist

Before selecting pattern, ask:

• Problem Complexity: Simple (<3 options) vs Complex (8+ dimensions)?
• Dependencies: Sequential steps vs Independent branches?
• Evaluation: Clear criteria vs Unclear how to judge?
• Solution Space: Known options vs Unknown territory?
• Output Needed: 1 best vs Multiple options vs Logical proof?
• Time Available: Quick (<20min) vs Thorough (60min+)?
• Confidence Required: Low (70%) vs High (90%+)?

Summary

Integrated Reasoning helps you choose the right cognitive tool:

• Tree of Thoughts: When you need the BEST solution (clear criteria, deep exploration)
• Breadth of Thought: When you need ALL options (unknown space, wide exploration)
• Self-Reflecting Chain: When you need LOGICAL proof (sequential steps, backtracking)
• Direct Analysis: When solution is OBVIOUS (simple problems, quick decisions)

Load the appropriate skill and follow its methodology for optimal results.

Most problems fit one pattern. Complex problems may need orchestration of multiple patterns sequentially or in parallel.

Remember: The right reasoning pattern depends on problem characteristics, not problem domain. A "database choice" could use ToT (if criteria clear), BoT (if exploring all options), or SRC (if migrating step-by-step).