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Whether Large Language Models (LLMs) exhibit covert psychological manipulation in complex human-AI interactions has garnered increasing safety concerns. However, existing AI safety benchmarks remain largely restricted to explicit rule compliance and static prompts, failing to capture the dynamic and covert nature of manipulative strategies in multi-turn dialogues. We introduce CogManip, a comprehensive benchmark that evaluates 15 manipulation strategy risks across 1,000 multi-turn interaction scenarios, validated by human experts. A systematic evaluation of 13 representative models, including frontier models like GPT-5.4 and DeepSeek-V3.2, reveals significant risk heterogeneities and illuminates the targeted direction for future defense. Further analysis of objective function perturbation reveals that DeepSeek-V3.2's manipulation tactics are highly sensitive to both negative and benign system prompts, demonstrating the critical necessity of prompt-based defense engineering and implicit goal auditing. CogManip offers a robust instrument and perspective for auditing the implicit psychological influence and dynamic strategy selection of modern LLMs.