Reliability Inference Drives Cue Extraction in Large Language Models Consuming External Reasoning Traces

Large language models increasingly consume external reasoning traces (tool logs, multi-agent outputs), yet must infer trace reliability to choose between independent computation and cue extraction. We introduce a controlled corruption paradigm that independently manipulates trace degradation and embedded answer cues. Across 28 experiments (71,168 trials) with GPT-4o and Claude, we observe reliability-gated cue extraction. In verifiable arithmetic, GPT-4o's wrong-cue following increases monotonically with corruption (0.5% to 8.5% at λ=0.8), while Claude remains near zero. Vulnerability is consumer-determined, amplified by cue salience (up to 21%) and naturalistic tool-log traces (29.1%), and does not require explicit "Answer:" markers. In unverifiable knowledge tasks, both models show elevated cue dependence (~14%). Verification-oriented prompts suppress cue following to 0%, providing a practical control principle for trace-consuming systems.