The reaction center consists of atoms in the product whose local properties are not identical to the corresponding atoms in the reactants. Prior studies on reaction center identification are mainly on semi-templated retrosynthesis methods. Moreover, they are limited to single reaction center identification. However, many reaction centers are comprised of multiple bonds or atoms in reality. We refer to it as the multiple reaction center. This paper presents RCsearcher, a unified framework for single and multiple reaction center identification that combines the advantages of the graph neural network and deep reinforcement learning. The critical insight in this framework is that the single or multiple reaction center must be a node-induced subgraph of the molecular product graph. At each step, it considers choosing one node in the molecular product graph and adding it to the explored node-induced subgraph as an action. Comprehensive experiments demonstrate that RCsearcher consistently outperforms other baselines and can extrapolate the reaction center patterns that have not appeared in the training set. Ablation experiments verify the effectiveness of individual components, including the beam search and one-hop constraint of action space.