Critical failures across all dimensions. The single tool 'execute_skill_action' has a reasonable name and description (89 chars), but the input schema is severely incomplete: only two parameters with minimal type info and no descriptions for either parameter. The schema lacks output documentation entirely, no return type, structure, or field definitions are visible. The tool definition appears inferred from client.py rather than explicitly registered in mcp_server.py. The mcp_server.py file contains only a stub that prints a JSON status message and does not actually implement MCP protocol message handling, tool registration, or request/response processing. No error handling, validation, or recovery guidance. No security considerations. This is a non-functional skeleton.

• Implement full MCP protocol in mcp_server.py: add stdin/stdout message loop, parse CallTool requests, invoke execute_skill_action, and return CallToolResult with proper error handling.
• Add descriptions to both input parameters. E.g., 'problem_statement: The mathematical or computational problem to solve using chain-of-thought reasoning (string, required)' and 'search_budget_tokens: Maximum thinking tokens allocated for deliberation (integer, 1-16384, default 4096)'.
• Document the output schema explicitly in mcp_server.py tool registration. Include all fields returned: deliberation_session_id (string), problem (string), allocated_thinking_tokens (integer), intermediate_verification_steps_count (integer), backtrack_and_correction_branches (integer), formal_mathematical_soundness_score_pct (number 0-100), final_concise_solution_verified (boolean).
• Add parameter constraints: search_budget_tokens should have min/max bounds (e.g., 256 - 16384) to prevent absurd values. Document in description.
• Implement error handling with actionable messages. E.g., if search_budget_tokens exceeds limit, return 'search_budget_tokens must be ≤ 16384; got {value}. Reduce and retry.' instead of a generic error.