In this paper, we report our methods and experiments for the TREC Conversational Assistance Track (CAsT) 2022. In this work, we aim to reproduce multi-stage retrieval pipelines and explore one of the potential benefits of involving mixed-initiative interaction in conversational passage retrieval scenarios: reformulating raw queries. Before the first ranking stage of a multi-stage retrieval pipeline, we propose a mixed-initiative query rewriting module, which achieves query rewriting based on the mixed-initiative interaction between the users and the system, as the replacement for the neural rewriting method. Specifically, we design an algorithm to generate appropriate questions related to the ambiguities in raw queries, and another algorithm to reformulate raw queries by parsing users' feedback and incorporating it into the raw query. For the first ranking stage of our multi-stage pipelines, we adopt a sparse ranking function: BM25, and a dense retrieval method: TCT-ColBERT. For the second-ranking step, we adopt a pointwise reranker: MonoT5, and a pairwise reranker: DuoT5. Experiments on both TREC CAsT 2021 and TREC CAsT 2022 datasets show the effectiveness of our mixed-initiative-based query rewriting (or query reformulation) method on improving retrieval performance compared with two popular reformulators: a neural reformulator: CANARD-T5 and a rule-based reformulator: historical query reformulator(HQE).