sequential-thinking

Purpose

Multi-variable analysis utility for decisions where factors are interdependent and order of reasoning matters. Receives a decision problem, classifies reversibility, detects cognitive biases, maps variable dependencies, processes them in dependency order, checks for second-order effects, and returns a structured decision tree with final recommendation. Stateless — no memory between calls.

Calls (outbound)

None — pure L3 reasoning utility.

Called By (inbound)

• debug (L2): multi-factor bugs with interacting causes
• plan (L2): complex architecture with many trade-offs
• brainstorm (L2): evaluating approaches with many variables

When to Use

Invoke this skill when:

• The decision has more than 3 interacting variables
• Choosing option A changes what options are valid for B and C
• Architecture decisions have cascading downstream effects
• Trade-off analysis where constraints eliminate entire solution branches

Do NOT use for simple linear analysis — problem-solver is more efficient for single-dimension reasoning.

Execution

Input

decision: string        — the decision or problem to analyze
variables: string[]     — (optional) pre-identified factors; if omitted, skill identifies them
constraints: string[]   — (optional) hard limits that eliminate options
goal: string            — (optional) success criteria or desired outcome

Step 0 — Reversibility Classification

Before investing analytical effort, classify the decision:

Type	Definition	Analytical Effort
Two-way door	Reversible, can iterate, low switching cost	Decide quickly, set review date. Light analysis.
One-way door	Irreversible, high stakes, costly to reverse	Full sequential analysis. Deep reasoning.
Partially reversible	Some aspects reversible, some not	Full analysis on irreversible aspects, light on reversible.

If two-way door → streamline: skip Step 4 (second-order) and Step 5 (bias cross-check). State reasoning.

Step 1 — Identify All Variables

List every factor that affects the decision. For each variable, record:

• Name and description
• Possible values or range
• Whether it is controllable (we can choose) or fixed (constraint from environment)

If the caller provided variables, validate and expand the list. If omitted, derive from the decision statement.

Step 2 — Map Dependencies

For each pair of variables, determine if a dependency exists:

• [A] constrains [B]: choosing a value for A limits valid values for B
• [A] influences [B]: A affects the cost/benefit calculation for B but does not eliminate options
• [A] independent of [B]: no relationship

Document dependencies as: [Variable A] → [Variable B]: [type and reason]

Identify which variables have the most outbound dependencies — those must be resolved first.

Step 3 — Evaluate in Dependency Order

Sort variables from most-constrained (fixed / most depended upon) to least-constrained (free / most flexible). Process in that order:

For each variable in sequence:

• State current known state of all previously resolved variables
• Evaluate valid options given those constraints
• Select the best option with explicit reasoning
• Record the conclusion and how it affects downstream variables

Do not jump ahead — each step must reference the conclusions of prior steps.

Running state block at each step:

State after Step N:
- [Variable A]: resolved to [value] because [reason]
- [Variable B]: resolved to [value] because [reason]
- Remaining: [Variable C], [Variable D]

Step 4 — Second-Order Effects Check

After all variables are resolved, apply second-order thinking:

For each resolved variable, ask: "And then what?"

Variable	First-Order Effect	Second-Order Effect	Risk Level
[A = value]	[immediate consequence]	[consequence of consequence]	low/medium/high

Flag any second-order effect that:

• Contradicts the goal stated in the input
• Creates a feedback loop (reinforcing or balancing)
• Affects stakeholders not considered in the analysis
• Would flip a previous variable's optimal value

If a dangerous second-order effect is found → revisit the affected variable with this new information.

Step 5 — Bias Cross-Check

Check the analysis for the 3 biases most dangerous to multi-variable decisions:

Bias	Detection Question	If Detected
Anchoring	Did the first variable we resolved disproportionately constrain all others? Would the result differ if we started from a different variable?	Re-evaluate with a different starting variable. Compare results.
Status Quo	Did we give an unfair advantage to "keep current approach" for any variable? Would we choose this if starting from scratch?	Evaluate current state with same rigor as alternatives.
Overconfidence	How confident are we in each variable's resolution? Are confidence intervals wide enough?	Assign explicit confidence % to each resolution. Flag any > 90% without strong evidence.

If bias is detected → note it in the report and state whether it changes the recommendation.

Step 6 — Synthesize

After all variables are resolved and cross-checked:

• Combine all per-step conclusions into a coherent final recommendation
• Identify any variables that remained ambiguous — state what additional information would resolve them
• Assess overall confidence: high (all variables resolved cleanly), medium (1-2 ambiguous), low (major uncertainty remains)
• Note the reversibility classification from Step 0 — if two-way door, include a review date

Step 7 — Report

Return the full decision tree and recommendation in the output format below.

Constraints

• Never evaluate variable B before all variables that constrain B are resolved
• If a dependency cycle is detected, flag it explicitly and break the cycle by treating one variable as a fixed assumption
• Use Sonnet — reasoning depth and coherence across many steps matters
• If more than 8 variables are identified, group related ones into composite variables to keep analysis tractable
• MUST classify reversibility (Step 0) before investing analytical effort
• MUST check for second-order effects on one-way door decisions
• MUST run bias cross-check on one-way door decisions

Output Format

## Sequential Analysis: [Decision]

### Reversibility: [two-way door / one-way door / partially reversible]
[One sentence reasoning. If two-way: "Light analysis — decide quickly, review in [timeframe]."]

### Variables Identified
| Variable | Possible Values | Type |
|----------|----------------|------|
| [A]      | [options]      | controllable / fixed |
| [B]      | [options]      | controllable / fixed |

### Dependency Map
- [A] → [B]: [type] — [reason]
- [C] → [A]: [type] — [reason]

### Step-by-Step Evaluation
1. **[Variable A]** (no dependencies — evaluate first)
   - Options: [x, y, z]
   - Reasoning: [why one is better given constraints]
   - Conclusion: **[chosen value]** (confidence: X%)
   - State: { A: [value] }

2. **[Variable B]** (depends on A = [value])
   - Options remaining: [filtered list]
   - Reasoning: [updated analysis given A's value]
   - Conclusion: **[chosen value]** (confidence: X%)
   - State: { A: [value], B: [value] }

...

### Second-Order Effects (one-way door only)
| Variable | First-Order | Second-Order | Risk |
|----------|------------|-------------|------|
| [A] | [effect] | [and then what?] | low/medium/high |

### Bias Check
- ⚠️ [Bias]: [detection result] → [action taken or "not detected"]

### Ambiguities
- [variable or factor that could not be fully resolved, and what information would resolve it]

### Final Recommendation
[synthesized conclusion incorporating all resolved variables, with confidence level]

- **Confidence**: high | medium | low
- **Key assumption**: [the most critical assumption this recommendation depends on]
- **Review date**: [when to revisit this decision, especially for two-way doors]

Sharp Edges

Failure Mode	Severity	Mitigation
Evaluating variable B before all variables constraining B are resolved	CRITICAL	Dependency order is mandatory — sort by constraint depth first
Dependency cycle detected but not flagged	HIGH	Break cycle by treating one variable as a fixed assumption — flag explicitly
More than 8 variables without grouping	MEDIUM	Group related variables — keep tractable, not exhaustive
Final recommendation missing confidence level	MEDIUM	Confidence (high/medium/low) is required — ambiguities drive confidence down
Full analysis on a two-way door decision	MEDIUM	Step 0 classifies reversibility — two-way doors get light analysis
Ignoring second-order effects on irreversible decisions	HIGH	Step 4 is mandatory for one-way doors — "and then what?"
Anchoring on first variable resolved	MEDIUM	Bias cross-check Step 5 — test if different starting variable changes result
No review date on reversible decisions	LOW	Two-way doors MUST include a review date — iterate, don't commit

Done When

• Reversibility classified (two-way / one-way / partial)
• All variables identified and typed (controllable vs. fixed)
• Dependency map documented (A constrains B, C influences D)
• Variables evaluated in dependency order with running state block and confidence % at each step
• Second-order effects checked (one-way door decisions)
• Bias cross-check completed (anchoring, status quo, overconfidence)
• Ambiguities listed with what information would resolve them
• Final recommendation emitted with confidence level and review date
• Sequential Analysis report in output format

Cost Profile

~500-1500 tokens input, ~500-1200 tokens output. Sonnet for reasoning depth.