Video agentic models have advanced challenging video-language tasks. However, most agentic approaches still heavily rely on greedy parsing over densely sampled video frames, resulting in high computational cost. We present VideoSeek, a long-horizon video agent that leverages video logic flow to actively seek answer-critical evidence instead of exhaustively parsing the full video. This insight allows the model to use far fewer frames while maintaining, or even improving, its video understanding capability. VideoSeek operates in a think-act-observe loop with a well-designed toolkit for collecting multi-granular video observations. This design enables query-aware exploration over accumulated observations and supports practical video understanding and reasoning. Experiments on four challenging video understanding and reasoning benchmarks demonstrate that VideoSeek achieves strong accuracy while using far fewer frames than prior video agents and standalone LMMs. Notably, VideoSeek achieves a 10.2 absolute points improvement on LVBench over its base model, GPT-5, while using 93% fewer frames. Further analysis highlights the significance of leveraging video logic flow, strong reasoning capability, and the complementary roles of toolkit design.