While large language models (LLMs) have shown strong performance in math and logic reasoning, their ability to handle combinatorial optimization (CO)—searching high-dimensional solution spaces under hard constraints—remains underexplored. To bridge the gap, we introduce NLCO, a Natural Language Combinatorial Optimization benchmark that evaluates LLMs on end-to-end CO reasoning: given a language-described decision-making scenario, the model must output a discrete solution without writing code or calling external solvers. NLCO covers 43 CO problems and is organized using a four-layer taxonomy of variable types, constraint families, global patterns, and objective classes, enabling fine-grained evaluation. We provide solver-annotated solutions and comprehensively evaluate LLMs by feasibility, solution optimality, and reasoning efficiency. Experiments across a wide range of modern LLMs show that high-performing models achieve strong feasibility and solution quality on small instances, but both degrade as instance size grows, even if more tokens are used for reasoning. We also observe systematic effects across the taxonomy: set-based tasks are relatively easy, whereas graph-structured problems and bottleneck objectives lead to more frequent failures. The benchmark dataset and code for data generation and evaluation are publicly available.

Clinicians read chain-of-thought (CoT) rationales as evidence of medical reasoning, but whether the visible chain plays that role is rarely tested. General-domain CoT-faithfulness probes ignore clinical cost, and medical LLM evaluations treat the chain as a black box. We close this gap with a medical perturbation audit: a 30-operator battery edits both the chain and the question with clinically motivated operators (severity reversal, negation flip, demographic swap, evidence ablation), paired with a chain-update × answer-flip joint analysis that classifies each model by its failure mode. Applied to 14 LLMs on four medical QA benchmarks, three independent tests converge: the Chain-Decoupling Rate (CDR; chain does not register the edit and the answer does not flip) is 72.9% panel-wide on M2/M4/M5 destructive edits, chain corruption leaves accuracy unchanged, and removing CoT prompting does not reduce accuracy. Two board-certified clinicians re-annotate N=197 perturbed questions; 98.5% leave the gold defensible. The pattern holds across medical and reasoning fine-tuning, scale, and the closed-source subset. Our framework and CDR provide a reusable yardstick for auditing whether medical CoT is faithful or merely documentation.