# From Good to Great: Improving Math Reasoning with Tool-Augmented Interleaf Prompting

arXiv: https://arxiv.org/abs/2401.05384 · HTML: https://mlsanity.com/paper/2401.05384/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 18 Dec 2023.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- LLM agents and tool use / [Tool learning and function calling](https://mlsanity.com/agents/tool-learning-and-function-calling/)

## Builds on (most cited first, 20 of 20)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [GLM-130B: An Open Bilingual Pre-trained Model](https://mlsanity.com/paper/2210.02414/) (2022)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [TALM: Tool Augmented Language Models](https://mlsanity.com/paper/2205.12255/) (2022)
- [ART: Automatic multi-step reasoning and tool-use for large language models](https://mlsanity.com/paper/2303.09014/) (2023)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Limitations of Language Models in Arithmetic and Symbolic Induction](https://mlsanity.com/paper/2208.05051/) (2022)
- [Breaking Language Barriers in Multilingual Mathematical Reasoning: Insights and Observations](https://mlsanity.com/paper/2310.20246/) (2023)
- [Large Language Models Meet Harry Potter: A Bilingual Dataset for Aligning Dialogue Agents with Characters](https://mlsanity.com/paper/2211.06869/) (2022)
- [Orca: A Few-shot Benchmark for Chinese Conversational Machine Reading Comprehension](https://mlsanity.com/paper/2302.13619/) (2023)

## Built on by (most cited first, 10 of 10)

- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [Compress to Impress: Unleashing the Potential of Compressive Memory in Real-World Long-Term Conversations](https://mlsanity.com/paper/2402.11975/) (2024)
- [GraphWiz: An Instruction-Following Language Model for Graph Problems](https://mlsanity.com/paper/2402.16029/) (2024)
- [ToolScope: Enhancing LLM Agent Tool Use through Tool Merging and Context-Aware Filtering](https://mlsanity.com/paper/2510.20036/) (2025)
- [Uncertainty Quantification for Hallucination Detection in Large Language Models: Foundations, Methodology, and Future Directions](https://mlsanity.com/paper/2510.12040/) (2025)
- [ResT: Reshaping Token-Level Policy Gradients for Tool-Use Large Language Models](https://mlsanity.com/paper/2509.21826/) (2025)
- [ControlMath: Controllable Data Generation Promotes Math Generalist Models](https://mlsanity.com/paper/2409.15376/) (2024)
- [RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library](https://mlsanity.com/paper/2504.20426/) (2025)
- [SafeMath: Safe Solutions for Unsafe Math Word Problems](https://mlsanity.com/paper/2603.25201/) (2026)
- [The Path Not Taken: Duality in Reasoning about Program Execution](https://mlsanity.com/paper/2604.20917/) (2026)

## Abstract (arXiv)

This paper investigates the performance of Large Language Models (LLMs) and Tool-augmented LLMs in tackling complex mathematical reasoning tasks. We introduce IMP-TIP: Improving Math Reasoning with Tool-augmented Interleaf Prompting, a framework that combines the strengths of both LLMs and Tool-augmented LLMs. IMP-TIP follows the ``From Good to Great" concept, collecting multiple potential solutions from both LLMs and their Tool-Augmented counterparts for the same math problem, and then selecting or re-generating the most accurate answer after cross-checking these solutions via tool-augmented interleaf prompting. The framework incorporates two key aspects: self-prompt and tool-augmented interleaf prompting (TIP). The former allows LLMs to autonomously refine and improve an initial prompt related to tool usage, while the latter enables LLMs to derive the final answer by dynamically analyzing the problem, cross-checking potential solutions, and revising previous reasoning hints in an interleaved manner. Experimental analysis shows that IMP-TIP achieves enhanced mathematical capabilities and outperforms traditional LLMs and tool-augmented LLMs in accuracy and reasoning diversity on math reasoning tasks. For instance, IMP-TIP can improve Tool-augmented ChatGPT on GSM8K-Hard from 56.0% to 65.2%.