While the emergence of powerful language models along with Chain-of-thought prompting has made automation more and more omnipresent, it sometimes demonstrates its weakness in long-term or multi-step logical reasoning. For example, users don't always get desirable answers for complex mathematical problems without human involvement. Against this background, we present the Manual Correction System (MCS) -- a human-in-the-loop system enhanced by Chain-of-Thought prompting, which explores how manual correction of sub-logics in rationales can improve LLM's reasoning performance. Moving one step forward, considering a system with human-in-the-loop involves more than having humans improve performance but also controlling the cost. Therefore, we post a Cost-utility Analysis Model for Human-in-the-Loop systems (CAMLOP) based on classical economics theory to analyze, quantify and balance the utility and the corresponding cost. We conduct experiments of MCS and CAMLOP with twelve datasets. A significant advantage w.r.t cost and utility proves its superiority over strong baselines.
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