Large-scale generative models like DeepSeek-R1 and OpenAI-O1 benefit substantially from chain-of-thought (CoT) reasoning, yet pushing their performance typically requires vast data, large model sizes, and full-parameter fine-tuning. While parameter‐efficient fine‐tuning (PEFT) helps reduce cost, most existing approaches primarily address domain adaptation or layer‐wise allocation rather than explicitly tailoring data and parameters to different response demands. Inspired by “Thinking, Fast and Slow,” which characterizes two distinct modes of thought—System 1 (fast, intuitive, often automatic) and System 2 (slower, more deliberative and analytic)—we draw an analogy that different “subregions” of an LLM’s parameters might similarly specialize for tasks that demand quick, intuitive responses versus those requiring multi-step logical reasoning. Therefore, we propose LoRA-PAR, a dual-system LoRA framework that partitions both data and parameters by System 1 or System 2 demands, using fewer yet more focused parameters for each task. Specifically, we classify task data via multi-model role-playing and voting, and partition parameters based on importance scoring, then adopt a two-stage fine-tuning strategy of training System 1 tasks with supervised fine-tuning (SFT) to enhance knowledge and intuition and refine System 2 tasks with reinforcement learning (RL) to reinforce deeper logical deliberation next. Extensive experiments show that the two-stage fine-tuning strategy, SFT and RL, lowers active parameter usage while matching or surpassing SOTA PEFT baselines.