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Recent advances in large language models (LLMs) have demonstrated the effectiveness of chain-of-thought (CoT) prompting. Few-Shot-CoT relies on task-specific, manually labeled demonstrations, limiting its generalization to unseen tasks. While Zero-Shot-CoT eliminates this reliance, it often underperforms. To address this, existing methods aim to automatically generate demonstrations in zero-shot settings. However, these generated demonstrations face challenges due to demonstration bias: 1) selected demonstrations may contain errors, and 2) they may not be suitable or representative enough for all questions. To mitigate these biases, we propose Global Coevolutionary Reasoning (GCR). The method first applies Zero-Shot-CoT to answer all questions, then clusters the results. For each cluster, a random sample is selected, and these selected samples serve as demonstrations for each other. The model then iteratively re-answers the questions and updates their rationales based on these demonstrations, enabling coevolutionary reasoning to progressively improve the quality of the answers. This process of random sampling and coevolutionary reasoning is repeated until all questions have been re-answered. Experimental results on ten datasets using GPT-3.5-turbo and GPT-4o-mini show that GCR outperforms baseline methods without any performance degradation caused by demonstration bias. Additionally, GCR is orthogonal to existing methods and can be seamlessly integrated with them.