Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas. However, their effectiveness in complex mathematical reasoning involving multi-step FOL deductions is still under-researched. While LLMs perform competitively on established mathematical reasoning benchmarks, they struggle with multi-step FOL tasks, as demonstrated by Deepseek-Prover-V2-7B’s low accuracy (4.2%) on our proposed theorem proving dataset. This issue arises from the limited exploration of diverse proof strategies and the potential for early reasoning mistakes to undermine entire proofs. To address these issues, we propose DREAM, a self-adaptive solution that enhances the Diversity and REAsonability of LLMs’ generation strategies. DREAM incorporates an Axiom-Driven Strategy Diversification mechanism to promote varied strategic outcomes and a Sub-Proposition Error Feedback to help LLMs reflect on and correct their proofs. Our contributions include pioneering advancements in LLMs’ mathematical reasoning through FOL theorem proving, introducing a novel inference stage solution that improves performance by 0.6% to 6.4%, and providing a curated dataset of 447 mathematical theorems in Lean 4 format for evaluation.

We present a novel three-stage framework leveraging Large Language Models (LLMs) within a risk-aware multi-agent system for automate strategy finding in quantitative finance. Our approach addresses the brittleness of traditional deep learning models in financial applications by: employing prompt-engineered LLMs to generate executable alpha factor candidates across diverse financial data, implementing multimodal agent-based evaluation that filters factors based on market status, predictive quality while maintaining category balance, and deploying dynamic weight optimization that adapts to market conditions. Experimental results demonstrate the robust performance of the strategy in Chinese & US market regimes compared to established benchmarks. Our work extends LLMs capabilities to quantitative trading, providing a scalable architecture for financial signal extraction and portfolio construction. The overall framework significantly outperforms all benchmarks with 53.17% cumulative return on SSE50 (Jan 2023 to Jan 2024), demonstrating superior risk-adjusted performance and downside protection on the market.