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Recent deep search agents built on large reasoning models (LRMs) excel at complex question answering by iteratively planning, acting, and gathering evidence, a capability known as search-integrated reasoning. However, mainstream approaches often train this ability using only outcome-based supervision, neglecting the quality of intermediate thoughts and actions. We introduce SRR-Judge, a framework for reliable step-level assessment of reasoning and search actions. Integrated into a modified ReAct-style rate-and-refine workflow, SRR-Judge provides fine-grained guidance for search-integrated reasoning and enables efficient post-training annotation. Using SRR-annotated data, we apply an iterative rejection sampling fine-tuning procedure to enhance the deep search capability of the base agent. Empirically, SRR-Judge delivers more reliable step-level evaluations than much larger models such as DeepSeek-V3.1, with its ratings showing strong correlation with final answer correctness. Moreover, aligning the policy with SRR-Judge annotated trajectories leads to substantial performance gains, yielding over a 10 percent average absolute pass@1 improvement across challenging deep search benchmarks.