The choice of a grasp plays a critical role in the success of downstream manipulation tasks. Consider a task of placing an object in a cluttered scene; the majority of possible grasps may not be suitable for the desired placement. In this paper, we study the synergy between the picking and placing of an object in a cluttered scene to develop an algorithm for task-aware grasp estimation. We present an object-centric action space that encodes the relationship between the geometry of the placement scene and the object to be placed in order to provide placement affordance maps directly from perspective views of the placement scene. This action space enables the computation of a one-to-one mapping between the placement and picking actions allowing the robot to generate a diverse set of pick-and-place proposals and to optimize for a grasp under other task constraints such as robot kinematics and collision avoidance. With experiments both in simulation and on a real robot we demonstrate that with our method, the robot is able to successfully complete the task of placement-aware grasping with over 89% accuracy in such a way that generalizes to novel objects and scenes.