Long horizon, contact-rich manipulation is inherently partially observable. This is as a single visual observation rarely captures a robot's full action context, including prior attempts, interactions, or progress. Consequently, standard visuomotor policies or vision-language-action models are prone to struggle in such tasks due to a lack of memory. To address this, we introduce Compressed Action Memory Policy (CAMP) based on the insight that a robot's own action history serves as a highly informative, self-supervised signal, enabling the policy to learn a robust, compact history representation. In our approach, we train a memory module to maintain a compressed representation of past actions, forcing it to encode a latent behavioral memory of all the robot's past interactions that can then be used to better contextualize future actions. This allows our approach to implicitly track generalized task progress and learn from failed attempts without any additional supervision, or external oversight. We evaluate CAMP across four real-robot setups and two novel simulation benchmarks: Memory-T-Bench and Memory-Manip-Bench. By demonstrating substantial gains over state-of-the-art baselines, CAMP is, to our knowledge, the first policy to demonstrate substantial success on contact-rich partially observable manipulation tasks purely through learned memory.