Ensuring the reliability of Large Language Models (LLMs) in complex reasoning tasks remains a formidable challenge, particularly in scenarios that demand precise mathematical calculations and knowledge-intensive open-domain generation. In this work, we introduce an uncertainty-aware framework designed to enhance the accuracy of LLM responses by systematically incorporating model confidence at critical decision points. We propose an approach that encourages multi-step reasoning in LLMs and quantify the confidence of intermediate answers such as numerical results in mathematical reasoning and proper nouns in open-domain generation. Then, the overall confidence of each reasoning chain is evaluated based on confidence of these critical intermediate steps. Finally, we aggregate the answer of generated response paths in a way that reflects the reliability of each generated content (as opposed to self-consistency in which each generated chain contributes equally to majority voting). We conducted extensive experiments in five datasets, three mathematical datasets and two open-domain datasets, using four LLMs. The results consistently validate the effectiveness of our novel confidence aggregation method, leading to an accuracy improvement of up to 7.4% and 5.8% over baseline approaches in math and open-domain generation tasks, respectively. Code is publicly available at https://github.com/ Aquasar11/CER.