Evaluating the symbolic reasoning of large language models (LLMs) calls for geometry benchmarks that require multi-step proofs grounded in both text and diagrams. However, existing benchmarks are often limited in scale and rarely provide visually grounded multiple-choice questions, limiting reliable evaluation of complex reasoning. We introduce GeoChallenge, a dataset of 90K automatically generated multiple-choice geometry proof problems, each requiring multi-step reasoning over aligned textual descriptions and diagrams. GeoChallenge provides fine-grained complexity ratings and formal language annotations to enable controlled evaluation. Experiments on multiple advanced LLMs show a clear performance gap between models and humans (the best-performing model, GPT-5-nano, achieves 75.89 exact match vs. 94.74 for humans). Further analysis also reveals three common failure patterns of LLMs: (1) exact match failures under the multiple-choice setting; (2) weak visual reliance; and (3) overextended reasoning without convergence.

Large Language Models (LLMs) often struggle with structural ambiguity in optimization problems, where a single problem admits multiple related but conflicting modeling paradigms, hindering effective solution generation. To address this, we propose Dual-Cluster Memory Agent (DCM-Agent) to enhance performance by leveraging historical solutions in a training-free manner. Central to this is Dual-Cluster Memory Construction. This agent assigns historical solutions to modeling and coding clusters, then distills each cluster’s content into three structured types: Approach, Checklist, and Pitfall. This process derives generalizable guidance knowledge. Furthermore, this agent introduces Memory-augmented Inference to dynamically navigate solution paths, detect and repair errors, and adaptively switch reasoning paths with structured knowledge. The experiments across seven optimization benchmarks demonstrate that DCM-Agent achieves an average performance improvement of 11%- 21%. Notably, our analysis reveals a “knowledge inheritance” phenomenon: memory constructed by larger models can guide smaller models toward superior performance, highlighting the framework’s scalability and efficiency.