Retrosynthesis prediction aims to identify reactants that can synthesize a given product molecule. Although molecular large language models (LLMs) have recently shown promising results, most existing methods either generate reactants directly or provide only generic product-level analysis, without explicitly reasoning about bond-disconnection strategies that justify specific reactant choices. This paper proposes RetroReasoner, a retrosynthetic reasoning model that captures chemists' strategic disconnection-based thinking. RetroReasoner is trained with supervised fine-tuning and reinforcement learning. For supervised fine-tuning, SyntheticRetro generates structured disconnection rationales paired with reactant predictions. For reinforcement learning, a round-trip reward evaluates predicted reactants by passing them through a forward synthesis model and rewarding predictions that reconstruct the original product. RetroReasoner can also be applied to multi-step retrosynthetic planning by incorporating it into a parallelized Monte Carlo tree search framework, reducing search time while increasing the number and diversity of valid synthetic pathways. Experimental results show that RetroReasoner outperforms prior baselines, including not only molecular LLMs but also retrosynthesis-specific expert models, and generates a broader range of feasible reactant proposals, especially for challenging reaction instances.