Recent theoretical work has proposed that hippocampus acts as a binding site for sensory stimuli and a task coordinate system, each represented in the entorhinal cortex. Since this coordinate system path-integrates, incoming sensory observations can be inferred rather than learned. Here, we show that (1) a similar mechanism can learn representations that predict actions rather than stimuli. This mechanism supports zero-shot action prediction – a significant departure from current theoretical frameworks for action-learning. (2) The learned representations resemble object-vector and landmark cells observed in the brain. (3) These representations can be controlled by simply gating memories, providing a potential mechanism for prefrontal cortex to select between goals. To achieve this, we extend the Tolman-Eichenbaum Machine (TEM) to include representations that both path-integrate and predict actions. In TEM, position representations are bound to sensory representations via hippocampal memories, with these memories retrievable via attractor dynamics. Here, we play the same trick but with position and action-predictive representations bound in hippocampus, meaning that action-predictive and position representations are arbitrarily composable. Now, 1) the same action-predictive representations can be learned, reused, and recombined at any position in space, thus actions can be predicted (and good behaviours taken!) in novel environments and contexts. 2) Memory retrieval can be modulated from prefrontal contextual signals, meaning the same action representation can be active in different positions depending on context. This allows different goals to be attended to within the same environment. In sum, we provide a mechanistic understanding of how action-predictive representations can be learned within the hippocampal-entorhinal system and controlled by prefrontal input. A companion paper shows that, once learned, these representations can be used to zero-shot optimal actions in complex structured environments. Together, these papers provide a theoretical foundation for the flexible context-dependent behaviour that is characteristic of animals but evades classical Reinforcement Learning algorithms.