feat: phase1 planning and video processing research

feat: system error field, calculator fix, target task IDs, course vs GAIA docs

Phase 0-2: HF Vision Integration Complete - Google Gemma 3 Selected

Add initial implementation for Phase 0 validation of HF Inference API with vision models

Stage 5: Performance optimization - retry logic, Groq integration, improved prompts

Fix: Tool name consistency across TOOLS registry and TOOL_FUNCTIONS

Stage 3: Core Logic Implementation - LLM Integration

Move test files from tests/ to test/ folder per project standard