Reinforcement learning-based approaches are widely studied in the literature for solving different control tasks for Connected and Autonomous Vehicles, from which this paper deals with the problem of lateral control of a dynamic nonlinear vehicle model, performing the task of lane-keeping. In this area, the appropriate formulation of the goals and environment information is crucial, for which the research outlines the importance of lookahead information, enabling to accomplish maneuvers with complex trajectories. Another critical part is the real-time manner of the problem. On the one hand, optimization or search based methods, such as the presented Monte Carlo Tree Search method, can solve the problem with the trade-off of high numerical complexity. On the other hand, single Reinforcement Learning agents struggle to learn these tasks with high performance, though they have the advantage that after the training process, they can operate in a real-time manner. Two planning agent structures are proposed in the paper to resolve this duality, where the machine learning agents aid the tree search algorithm. As a result, the combined solution provides high performance and low computational needs