Existing benchmarks treat multi-turn conversation and reasoning-intensive retrieval separately, yet real-world information seeking requires both. To bridge this gap, we present a benchmark for reasoning-based conversational information retrieval comprising 707 conversations (2,971 turns) across eleven domains. To ensure quality, our Decomposition-and-Verification framework transforms complex queries into fact-grounded multi-turn dialogues through multi-level validation, where atomic facts are verified against sources and explicit retrieval reasoning is generated for each turn. Comprehensive evaluation reveals that combining conversation history with reasoning doubles retrieval performance (Baseline .236 $\rightarrow$ History+Reasoning .479 nDCG@10), while reasoning-specialized models substantially outperform dense encoders. Despite these gains, further analysis highlights that implicit reasoning remains challenging, particularly when logical connections are not explicitly stated in the text.