Inspired by the dual-process theory of human cognition from \textit{Thinking, Fast and Slow}, we introduce \textbf{PRIME} (Planning and Retrieval-Integrated Memory for Enhanced Reasoning), a multi-agent reasoning framework that dynamically integrates \textbf{System 1} (fast, intuitive thinking) and \textbf{System 2} (slow, deliberate thinking). PRIME first employs a Quick Thinking Agent (System 1) to generate a rapid answer; if uncertainty is detected, it then triggers a structured System 2 reasoning pipeline composed of specialized agents for \textit{planning}, \textit{hypothesis generation}, \textit{retrieval}, \textit{information integration}, and \textit{decision-making}. This multi-agent design faithfully mimics human cognitive processes and enhances both efficiency and accuracy. Experimental results with LLaMA 3 models demonstrate that PRIME enables open-source LLMs to perform competitively with state-of-the-art closed-source models like GPT-4 and GPT-4o on benchmarks requiring multi-hop and knowledge-grounded reasoning. This research establishes PRIME as a scalable solution for improving LLMs in domains requiring complex, knowledge-intensive reasoning.