Extended Thinking & Adaptive Budget Implementation

Implement the `Reflect` and `PlanAction` nodes in your LangGraph with extended thinking capabilities. Detail how GPT-5 Pro will perform self-correction, error analysis (e.g., from UI exceptions), and dynamic replanning. Incorporate adaptive reasoning budgets by outlining how the agent will increase/decrease its 'thinking budget' (e.g., number of LLM calls, retry attempts, depth of reflection) based on recent task success or failure, and how session length constraints will be proactively managed. Provide concrete code snippets for these node implementations.