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Age of Information (AoI) is an emerging metric used to assess the timeliness of information, gaining research interest in real-time multicast applications such as video streaming and metaverse platforms. In this paper, we consider a dynamic multicast network with energy constraints, where our objective is to minimize the expected time-average AoI through energy-constrained multicast routing and scheduling. The inherent complexity of the problem, given the NP-hardness and intertwined scheduling and routing decisions, makes existing approaches inapplicable. To address these challenges, we decompose the original problem into two subtasks, each amenable to reinforcement learning (RL) methods. Subsequently, we propose an innovative framework based on graph attention networks (GATs) to effectively capture graph information with superior generalization capabilities. To validate our framework, we conduct experiments on three datasets including a real-world dataset called AS-733, and show that our proposed scheme reduces the energy consumption by while achieving a similar AoI compared to baselines.