Lead optimization in drug discovery requires improving therapeutic properties while ensuring that molecular modifications correspond to feasible synthetic routes. Existing approaches either prioritize property scores without enforcing synthesizability, or rely on expensive enumeration over large reaction networks, while direct application of Large Language Models (LLMs) to molecular generation frequently produces chemically invalid structures. We introduce MolReAct, a framework that formulates lead optimization as a Markov Decision Process over a synthesis-constrained action space defined by validated reaction templates. A tool-augmented LLM agent serves as a dynamic reaction environment, invoking specialized chemical analysis tools to identify reactive sites and functional groups and proposing a compact set of chemically grounded transformations from matched templates. A dedicated policy model trained via Group Relative Policy Optimization (GRPO) selects among these constrained actions to maximize long-term oracle reward across multi-step trajectories, with a SMILES-based caching mechanism reducing end-to-end optimization time by approximately 43%. Across 13 property optimization tasks from the Therapeutic Data Commons and one structure-based docking task, MolReAct achieves an average Top-10 score of 0.571, the highest among all baselines, ranking first or second on 13 of 14 tasks and attaining the best sample efficiency on 9 of 14 tasks. By grounding every optimization step in validated reaction templates, MolReAct produces molecules that are not only property-improved but each accompanied by an explicit template-grounded synthetic pathway.