This thesis presents a novel and scalable approach for Reactive Task and Motion Planning. We consider changing environments with uncontrollable agents, where the robot needs a policy to respond correctly in the infinite interaction with the environment. Our approach operates on task and motion domains that combine actions over discrete states with continuous, collision-free paths. We synthesize a policy by iteratively verifying and searching for a policy candidate. For efficient verification, we employ Satisfiability Modulo Theories (SMT) solvers using a new extension of proof rules for Temporal Property Verification. For efficient policy search, we apply domain-specific heuristics to generalize verification failures. Furthermore, the SMT solver enables quantitative specifications such as energy limits. We benchmark our policy synthesizer in a mobile manipulation domain, showing that our approach offers better scalability compared to a state-of-the-art robotic synthesis tool in the tested benchmarks and demonstrating order-of-magnitude speedup from our heuristics.