Recent search-augmented LLMs trained with reinforcement learning (RL) can interleave searching and reasoning for multi-hop reasoning tasks. However, they face two critical failure modes as the accumulating context becomes flooded with both crucial evidence and irrelevant information: (1) ineffective search chain construction that produces incorrect queries or omits retrieval of critical information, and (2) reasoning hijacking by peripheral evidence that causes models to misidentify distractors as valid evidence. To address these challenges, we propose **D$^2$Plan**, a **D**ual-agent **D**ynamic global **Plan**ning paradigm for complex retrieval-augmented reasoning. **D$^2$Plan** operates through the collaboration of a *Reasoner* and a *Purifier*: the *Reasoner* constructs explicit global plans during reasoning and dynamically adapts them based on retrieval feedback; the *Purifier* assesses retrieval relevance and condenses key information for the *Reasoner*. We further introduce a two-stage training framework consisting of supervised fine-tuning (SFT) cold-start on synthesized trajectories and RL with plan-oriented rewards to teach LLMs to master the **D$^2$Plan** paradigm. Extensive experiments demonstrate that **D$^2$Plan** enables more coherent multi-step reasoning and stronger resilience to irrelevant information, thereby achieving superior performance on challenging QA benchmarks.