The CoVR-R challenge evaluates composed video retrieval, where a system must retrieve a target video from a large gallery given a reference video and a textual edit instruction. This setting is not a standard video-text retrieval problem: the query is defined by both the visual evidence in the source video and the transformation implied by the edit. A strong embedding model can provide scalable candidate recall, but it may under-express target-side consequences such as state changes, action replacement, object preservation, or temporal consistency. A pairwise multimodal reranker can verify such details more directly, but exhaustive reranking over the full gallery is computationally infeasible. We present $\mathbb{R}^3$, a zero-shot composed video retrieval pipeline built around Reasoning-guided Recalling and Reranking. The core idea is to turn the source-edit query into a reasoning-grounded retrieval program rather than treating the edit text as a short caption. First, the model generates a reasoning trace that describes the expected target video after applying the edit. Then the trace is encoded together with the source video as a reasoning-augmented query, and its retrieval score is fused with the base composed query through an agreement-gated residual rule. At last, a re-ranker verifies the recalled candidates with direct source-candidate comparison. Experiments have demonstrated the effectiveness of our method in addressing this challenge. Codes are available on https://github.com/Lee-zixu/R-3.