Video color grading is a critical post-production process that transforms flat, log-encoded raw footage into emotionally resonant cinematic visuals. Existing automated methods act as static, black-box executors that directly output edited pixels, lacking both interpretability and the iterative control required by professionals. We introduce LumiVideo, an agentic system that mimics the cognitive workflow of professional colorists through four stages: Perception, Reasoning, Execution, and Reflection. Given only raw log video, LumiVideo autonomously produces a cinematic base grade by analyzing the scene's physical lighting and semantic content. Its Reasoning engine synergizes an LLM's internalized cinematic knowledge with a Retrieval-Augmented Generation (RAG) framework via a Tree of Thoughts (ToT) search to navigate the non-linear color parameter space. Rather than generating pixels, the system compiles the deduced parameters into industry-standard ASC-CDL configurations and a globally consistent 3D LUT, analytically guaranteeing temporal consistency. An optional Reflection loop then allows creators to refine the result via natural language feedback. We further introduce LumiGrade, the first log-encoded video benchmark for evaluating automated grading. Experiments show that LumiVideo approaches human expert quality in fully automatic mode while enabling precise iterative control when directed.