Large language model (LLM) agents face fundamental limitations in long-horizon reasoning due to finite context windows, making effective memory management critical.Existing methods typically handle long-term memory (LTM) and short-term memory (STM) as separate components, relying on heuristics or auxiliary controllers, which limits adaptability and end-to-end optimization.In this paper, we propose Agentic Memory (AgeMem), a unified framework that integrates LTM and STM management directly into the agent's policy.AgeMem exposes memory operations as tool-based actions, enabling the LLM agent to autonomously decide what and when to store, retrieve, update, summarize, or discard information.To train such unified behaviors, we propose a three-stage progressive reinforcement learning strategy and design a step-wise GRPO to address sparse and discontinuous rewards induced by memory operations.Experiments on five long-horizon benchmarks demonstrate that AgeMem consistently outperforms strong memory-augmented baselines across multiple LLM backbones, achieving improved task performance, higher-quality long-term memory, and more efficient context usage.