Video understanding with multimodal large language models (MLLMs) remains challenging due to the long token sequences of videos, which contain extensive temporal dependencies and redundant frames. Existing approaches typically treat MLLMs as passive recognizers, processing entire videos or uniformly sampled frames without adaptive reasoning. Recent agent-based methods introduce external tools, yet still depend on manually designed workflows and perception-first strategies, resulting in inefficiency on long videos. We present EVA, an Efficient Reinforcement Learning framework for End-to-End Video Agent, which enables planning-before-perception through iterative summary-plan-action-reflection reasoning. EVA autonomously decides what to watch, when to watch, and how to watch, achieving query-driven and efficient video understanding. To train such agents, we design a simple yet effective three-stage learning pipeline - comprising supervised fine-tuning (SFT), Kahneman-Tversky Optimization (KTO), and Group Relative Policy Optimization (GRPO) - that bridges supervised imitation and reinforcement learning. We further construct high-quality datasets for each stage, supporting stable and reproducible training. We evaluate EVA on six video understanding benchmarks, demonstrating its comprehensive capabilities. Compared with existing baselines, EVA achieves a substantial improvement of 6-12% over general MLLM baselines and a further 1-3% gain over prior adaptive agent methods.