Time series forecasting is fundamental to temporal data mining, yet numerical models often struggle to account for changing contextual factors. A key challenge is determining when contextual evidence should guide forecast revisions while maintaining consistency with temporal patterns and domain knowledge. To address this, we propose CastFSR, a fast--slow--reflect agentic framework for context-aware time series forecasting. Fast-thinking forecasting analyzes numerical patterns, selects a suitable forecaster, and constructs a data-driven forecast prior. Slow deliberative reasoning incorporates relevant contextual evidence to selectively refine this prior, while reflective evaluation checks the revised forecast against temporal patterns, contextual evidence, and domain constraints. A shared state maintains forecasting priors, contextual evidence, intermediate forecasts, and feedback across stages. CastFSR supports both training-free LLM coordination and two-stage post-training for compact LLM coordinators. Workflow-aware trajectory distillation (WATD) learns state-conditioned tool use and forecasting decisions from teacher trajectories, while trajectory-level policy optimization (TLPO) further improves the coordinator through reinforcement learning guided by forecasting accuracy and workflow feedback. Experiments on multiple real-world datasets under an offline evaluation protocol using historical context demonstrate competitive performance against representative baselines. Our code is available at https://github.com/Xiaoyu-Tao/CastFSR.

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