This paper addresses the problem of goal recognition in multi-agent environments. Unlike previous research on passive goal recognition, we focus on active goal recognition (AGR) and propose a strategic information gathering method to reduce uncertainty. Based on a probabilistic framework, we present a solution that integrates a joint belief updating mechanism and a Monte Carlo Tree Search (MCTS) algorithm. This enables efficient planning and inference of hidden goals of agents without domain-specific knowledge. Experimental results in a grid-based domain demonstrate that the proposed joint belief updating mechanism outperforms passive goal recognition, and the domain-independent MCTS algorithm performs similarly to domain-specific greedy baselines. This demonstrates that the proposed solution is a practical and robust goal inference framework, laying the foundation for more interactive and adaptive multi-agent systems.