A web application needs to maintain a real-time, fixed-size summary of a user's browsing session to provide personalized recommendations. The session consists of a long sequence of events, where each event is a (product_ID, action_type) pair (e.g., ('P123', 'view'), ('P456', 'add_to_cart')). Given the constraint of using a constant amount of memory regardless of session length, explain how the recurrent cache mechanism, defined by the formula New_Memory = Update(Current_Event, Previous_Memory), would be applied to solve this problem. In your explanation, specify what Current_Event, Previous_Memory, and New_Memory would represent in this specific scenario.