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Prior studies on intelligent reflecting surface (IRS) have mostly considered wireless communication systems aided by a single passive IRS, which, however, has limited control over wireless propagation environment and suffers from product-distance path-loss. To address these issues, we propose in this paper a new hybrid active/passive IRS aided wireless communication system, where an active IRS and multiple passive IRSs are deployed to assist the communication between a base station (BS) and a remote user in complex environment, by establishing a multihop reflection path across active/passive IRSs. In particular, the active IRS enables signal reflection with power amplification, thus effectively compensating the severe path-loss in the multi-reflection path. To maximize the achievable rate at the user, we first design the optimal beamforming of the BS and selected (active/passive) IRSs for a given multi-reflection path, and then propose an efficient algorithm to obtain the optimal multi-reflection path by using the path decomposition method and graph theory. We show that the active IRS should be selected to establish the beam routing path when its amplification power and/or number of active reflecting elements are sufficiently large. Last, numerical results demonstrate the effectiveness of the proposed hybrid active/passive IRS beam routing design as compared to the benchmark scheme with passive IRSs only.