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recursive_thinking

Apply recursive strategies to structure problem-solving with base and recursive cases, analyze complexity, and optimize solutions.

Instructions

Applying recursive strategies to solve problems with base and recursive cases, including optimizations.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
domainNoThe domain or field this problem belongs to (e.g., 'algorithms', 'data structures').
problemYesA clear and comprehensive description of the problem to be solved recursively.
baseCasesYesThe base cases that terminate the recursion.
problemIdNoA unique identifier for this recursive problem analysis.
testCasesNoKey test cases for validating the recursive solution.
invariantsNoProperties that remain true throughout the recursive calls.
optimizationsNoPossible optimizations for the recursive solution.
commonMistakesNoCommon mistakes when implementing this recursive solution.
inputSizeLimitNoPractical limit on input size before stack overflow.
recursiveCasesYesThe recursive cases that break down the problem.
similarProblemsNoOther problems that use similar recursive patterns.
recursionPatternNoThe pattern of recursion used.
stackOverflowRiskNoRisk of stack overflow for typical inputs.
complexityAnalysisNoDetailed complexity analysis of the recursive solution.
learningObjectivesNoWhat can be learned from this recursive analysis.
iterativeAlternativesNoAlternative iterative solutions.
terminationConditionsYesAll conditions under which the recursion will terminate.
tailRecursionOptimizableNoWhether the recursion can be optimized with tail recursion.
Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations provided, the description must fully disclose behavioral traits. It only says 'applying recursive strategies' and mentions optimizations, but does not explain what the tool actually does (e.g., mutate state, return analysis, require specific permissions) or any side effects or constraints.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness2/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is a single sentence, which is not verbose, but it lacks substance and does not earn its place by providing necessary information. It is underspecified rather than concise.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complex input schema (18 parameters, nested objects) and no output schema, the description should explain how the tool processes inputs and what it returns. It only gives a high-level purpose, leaving significant gaps in understanding.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so each parameter has a description in the schema. The tool description adds no additional meaning beyond the schema, which is acceptable at baseline 3.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose3/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description states it applies recursive strategies to solve problems with base and recursive cases, including optimizations. This gives a general sense but lacks specifics about what the tool does (e.g., analyze, generate, or solve) and does not differentiate from sibling tools like sequential_thinking or problem_decomposition.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance on when to use this tool versus alternatives such as collaborative_reasoning or critical_thinking. The description does not mention context, prerequisites, or exclusions, leaving the agent to infer usage from the name alone.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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