Current plan-based reasoning methods improve large language models (LLMs) by inserting a planning stage before execution, giving rise to the **question → plan → cot** paradigm. While effective, a closer examination reveals an inherent paradigm-level gap: both the planning and its execution stages decide *how to solve* a problem, while the prior question of *what to solve*; recognizing the problem type, the applicable tools, and the foreseeable pitfalls; remains entirely implicit. To bridge this gap, we propose **PPC** (**P**replan-**P**lan-**C**oT), a framework that introduces an explicit problem-understanding stage, the *preplan*, yielding a new **question → preplan → plan → cot** paradigm. Realizing this paradigm requires safeguarding the conceptual integrity of preplan at both ends. Specifically, we design a three-stage synthesis pipeline with a *spoiler-score detector* that filters out leakage and spoiler failures to build clean preplan supervision, and a composite GRPO reward enforces that the generated plan genuinely follows from the preplan. Experiments across four backbones and five mathematical reasoning benchmarks show that PPC achieves the best results on 39 of 40 metrics, improving *maj@16* and *pass@16* by +2.23 and +3.06 over the strongest baseline without introducing additional inference token overhead.

Recent studies reveal that large language models (LLMs) exhibit limited logical reasoning abilities in mathematical problem-solving, instead often relying on pattern-matching and memorization. We systematically analyze this limitation, focusing on logical relationship understanding, which is a core capability underlying genuine logical reasoning, and reveal that errors related to this capability account for over 90% of incorrect predictions, with Chain-of-Thought Supervised Fine-Tuning (CoT-SFT) failing to substantially reduce these errors. To address this bottleneck, we propose First-Step Logical Reasoning (FSLR), a lightweight training framework targeting logical relationship understanding. Our key insight is that the first planning step-identifying which variables to use and which operation to apply-encourages the model to derive logical relationships directly from the problem statement. By training models on this isolated step, FSLR provides explicit supervision for logical relationship understanding, unlike CoT-SFT which implicitly embeds such relationships within complete solution trajectories. Extensive experiments across multiple models and datasets demonstrate that FSLR consistently outperforms CoT-SFT under both in-distribution and out-of-distribution settings, with average improvements of 3.2% and 4.6%, respectively. Moreover, FSLR achieves 4-6× faster training and reduces training token consumption by over 80%.