Search and recommendation (S&R) are fundamental components of modern online platforms, yet effectively leveraging search behaviors to improve recommendation remains a challenging problem. User search histories often contain noisy or irrelevant signals that can even degrade recommendation performance, while existing approaches typically encode S&R histories either jointly or separately without explicitly identifying which search behaviors are truly useful. Inspired by the human decision-making process, where one first identifies recommendation intent and then reasons about relevant evidence, we design a latent cross reasoning framework that first encodes user S&R histories to capture global interests and then iteratively reasons over search behaviors to extract signals beneficial for recommendation. Contrastive learning is employed to align latent reasoning states with target items, and reinforcement learning is further introduced to directly optimize ranking performance. Extensive experiments on public benchmarks demonstrate consistent improvements over strong baselines, validating the importance of reasoning in enhancing search-aware recommendation.