# Plan before Solving: Problem-Aware Strategy Routing for Mathematical Reasoning with LLMs

arXiv: https://arxiv.org/abs/2509.24377 · HTML: https://mlsanity.com/paper/2509.24377/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 6 of 6)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [DeepSeek-VL: Towards Real-World Vision-Language Understanding](https://mlsanity.com/paper/2403.05525/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Deliberation on Priors: Trustworthy Reasoning of Large Language Models on Knowledge Graphs](https://mlsanity.com/paper/2505.15210/) (2025)

## Built on by (most cited first, 3 of 3)

- [When Do LLMs Reason? A Dynamical Systems View via Entropy Phase Transitions](https://mlsanity.com/paper/2605.22873/) (2026)
- [Strategy Executability in Mathematical Reasoning: Leveraging Human-Model Differences for Effective Guidance](https://mlsanity.com/paper/2602.22583/) (2026)
- [Beyond Accuracy: Evaluating Strategy Diversity in LLM Mathematical Reasoning](https://mlsanity.com/paper/2605.09292/) (2026)

## Abstract (arXiv)

Existing methods usually leverage a fixed strategy, such as natural language reasoning, code-augmented reasoning, tool-integrated reasoning, or ensemble-based reasoning, to guide Large Language Models (LLMs) to perform mathematical reasoning. Our analysis reveals that the single strategy cannot adapt to problem-specific requirements and thus overlooks the trade-off between effectiveness and efficiency. To address these issues, we propose Planning and Routing through Instance-Specific Modeling (PRISM), a novel framework that decouples mathematical reasoning into two stages: strategy planning and targeted execution. Specifically, we first curate a multi-strategy preference dataset, which we call MathStrat, capturing correctness, process quality, and computational efficiency for each problem--strategy pair. Then, we train a lightweight Strategy Adapter based on the dataset to obtain confidence distributions over the mentioned four reasoning strategies. At inference time, an adaptive routing policy dynamically tailors the reasoning approach based on predictor confidence. It directs the model to use single-strategy execution for high-confidence predictions, dual-strategy verification for competitive scenarios, or comprehensive multi-strategy exploration for uncertain cases. Extensive experiments across five mathematical reasoning benchmarks demonstrate that PRISM consistently outperforms individual strategies and ensemble baselines, achieving improvements ranging from 0.9% to 7.6% across different base models. The adaptive routing approach shows particularly strong benefits for mathematical reasoning tasks across diverse model architectures. Our code is released at https://github.com/reml-group/PRISM.