Getting language models to reason correctly about code requires training on data where each reasoning step can be checked. Current synthetic Chain-of-Thought (CoT) training data often consists of plausible-sounding explanations generated by teacher models, and not verifiable accounts of actual program behavior. Models trained on such data learn logically flawed reasoning patterns despite syntactic correctness. To address this, we build a pipeline that generates execution-trace-verified CoT rationales by instrumenting code to capture traces, narrating them into natural language, and cross-checking each narration against the original trace. We systematically create 54,000 verified, bi-directional rationales that teach models to reason both forward (input$\rightarrow$output) and backward (output$\rightarrow$input). Models fine-tuned on our verified data achieve substantial improvements, with a peak gain of +26.6 on LiveCodeBench-Exec, +22.2 on CruxEval, and +19.5 on HumanEval across our fine-tuned models, demonstrating that verification quality directly determines both reasoning and code generation capabilities. Complete synthesis pipeline is avilable as open-source: https://github.com/IBM/verified-code-cot/