In interactions between automated vehicles (AVs) and crossing pedestrians, modeling implicit vehicle communication is crucial. In this work, we present a combined prediction and planning approach that allows to consider the influence of the planned vehicle behavior on a pedestrian and predict a pedestrian's reaction. We plan the behavior by solving two consecutive optimal control problems (OCPs) analytically, using variational calculus. We perform a validation step that assesses whether the planned vehicle behavior is adequate to trigger a certain pedestrian reaction, which accounts for the closed-loop characteristics of prediction and planning influencing each other. In this step, we model the influence of the planned vehicle behavior on the pedestrian using a probabilistic behavior acceptance model that returns an estimate for the crossing probability. The probabilistic modeling of the pedestrian reaction facilitates considering the pedestrian's costs, thereby improving cooperative behavior planning. We demonstrate the performance of the proposed approach in simulated vehicle-pedestrian interactions with varying initial settings and highlight the decision making capabilities of the planning approach.