Automatically solving optimization problems from natural language descriptions with both efficiency and reliability is highly desirable but remains challenging. Language model hallucinations and the limited availability of labeled datasets often result in misaligned formulations, code errors, and feasibility failures We propose UMCTS, an Uncertainty-aware Monte Carlo Tree Search framework that combines the language understanding capability of large language models with the reliability of well-established solvers. UMCTS structures the solution process into four stages: global instruction, assumptions, mathematical formulation, and solver code generation. It employs Monte Carlo Tree Search with semantic-equivalence pruning, prior-guided exploration, and solver-based feasibility checks. An LLM judge provides numerical reward signals, qualitative error information, and uncertainty estimates. These signals are backpropagated to guide the search and flag unreliable outputs. Across six public benchmarks, UMCTS achieves state-of-the-art solution accuracy, improves efficiency by reducing token usage.

Chain-of-Thought (CoT) reasoning has driven recent gains of large language models (LLMs) on reasoning-intensive tasks by externalizing intermediate steps. However, excessive or redundant reasoning — so-called overthinking — can increase inference costs and lead LLMs toward incorrect conclusions. In this paper, we present REFRAIN ( ̲REFlective- ̲Redundancy for  ̲Adaptive  ̲INference), a training-free framework that adaptively determines when to stop reasoning to mitigate overthinking. REFRAIN integrates a two-stage stop discriminator to identify reflective yet redundant reasoning and a sliding-window Upper Confidence Bound (SW-UCB) multi-armed bandit controller to dynamically adjust stopping thresholds according to problem difficulty without supervision or fine-tuning. Across four representative benchmarks and two model families, REFRAIN reduces token usage by 20-55% while maintaining or improving accuracy compared to standard CoT prompting. Extensive ablation and robustness analyses demonstrate its stability across models, scorers, and prompt variations. In summary, our findings highlight when-to-stop as a new and practical axis of test-time scaling — enabling models to reason not just more, but just enough.