We developed a novel two-step decision task for mice that disambiguates state predictions from reward predictions in neural activity and model-based from model-free control in behavior. Calcium imaging indicated that ACC represented a set of variables required for model-based control: the state-action space of the task, the current configuration of transition probabilities linking actions to states, predicted future states given chosen actions, and whether state transitions matched these predictions. Consistent with these findings, optogenetic inhibition of ACC on individual trials reduced the influence of action-state transitions on subsequent choice, without affecting the direct reinforcing effect of reward. The strength of this inhibition effect strongly correlated across subjects with their use of model-based RL. These data suggest that the ACC is a critical controller of model-based strategies and, more specifically, reveal that the ACC is involved in predicting future states given chosen actions.