Task and Motion Planning (TAMP) is a computationally challenging roboticsproblem due to the tight coupling of discrete symbolic planning and continuousgeometric planning of robot motions. In particular, planning manipulation tasksin complex 3D environments leads to a large number of costly geometric plannerqueries to verify the feasibility of considered actions and plan their motions. Toaddress this issue, we propose Geometric Reasoning Networks (GRN), a graphneural network (GNN)-based model for action and grasp feasibility prediction,designed to significantly reduce the dependency on the geometric planner. More-over, we introduce two key interpretability mechanisms: inverse kinematics (IK)feasibility prediction and grasp obstruction (GO) estimation. These modules notonly improve feasibility predictions accuracy, but also explain why certain actionsor grasps are infeasible, thus allowing a more efficient search for a feasible solu-tion. Through extensive experimental results, we show that our model outperformsstate-of-the-art methods, while maintaining generalizability to more complex en-vironments, diverse object shapes, multi-robot settings, and real-world robots.