Large language model (LLM) personalization aims to align model outputs with individuals' unique preferences and opinions. While recent efforts have implemented various personalization methods, a unified theoretical framework that can systematically understand the drivers of effective personalization is still lacking. In this work, we integrate the well-established cognitive dual-memory model into LLM personalization, by mirroring episodic memory to historical user engagements and semantic memory to long-term, evolving user beliefs. Specifically, we systematically investigate memory instantiations and introduce a unified framework, PRIME, using episodic and semantic memory mechanisms. We further augment PRIME with a novel personalized thinking capability inspired by the slow thinking strategy. Moreover, recognizing the absence of suitable benchmarks, we introduce CMV dataset specifically designed to evaluate long-context personalization. Extensive experiments validate PRIME's effectiveness across both long- and short-context scenarios. Further analysis confirms that PRIME effectively captures dynamic personalization beyond mere popularity biases.