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Design Gemini-powered Reasoning Agent

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Linked challenge: Mathematical Proof Assistant

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Linked challenge
Mathematical Proof Assistant

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Design a LlamaIndex agent that leverages Gemini 2.5 Pro for its primary reasoning engine. The agent should be able to receive a mathematical statement, query the `VectorStoreIndex` for relevant context, and then use Gemini to construct a step-by-step proof. Implement at least two tools within the LlamaIndex agent: one to `search_math_index` (which queries your ChromaDB-backed `VectorStoreIndex`) and another to `output_final_proof` (which formats the Gemini-generated proof). Include the agent initialization and tool definitions.

Adaptation plan

Keep the source stable, then change the prompt in a predictable order so the next run is easier to evaluate.

Keep stable

Hold the task contract and output shape stable so generated implementations remain comparable.

Tune next

Update libraries, interfaces, and environment assumptions to match the stack you actually run.

Verify after

Test failure handling, edge cases, and any code paths that depend on hidden context or secrets.