Recent LLMs have demonstrated sophisticated problem-solving capabilities on various benchmarks through advanced reasoning algorithms. However, the key research question of identifying reasoning steps that balance complexity and computational efficiency remains unsolved. Recent research has increasingly drawn upon psychological theories to explore strategies for optimizing cognitive pathways. The LLM's final outputs and intermediate steps are regarded as System 1 and System 2, respectively. However, an in-depth exploration of the System 2 reasoning is still lacking. Therefore, we propose a novel psychologically backed Scaffold Reasoning framework for code debugging, which encompasses the Scaffold Stream, Analytic Stream, and Integration Stream. The construction of reference code within the Scaffold Stream is integrated with the buggy code analysis results produced by the Analytic Stream through the Integration Stream. Our framework achieves an 88.91% pass rate and an average inference time of 5.36 seconds per-problem on DebugBench, outperforming other reasoning approaches across various LLMs in both reasoning accuracy and efficiency. Further analyses elucidate the advantages and limitations of various cognitive pathways across varying problem difficulties and bug types. Our findings also corroborate the alignment of the proposed Scaffold Reasoning framework with human cognitive processes.