Adaptive task planning is fundamental to ensuring effective and seamless human-robot collaboration. This paper introduces a robot task planning framework that takes into account both human leading/following preferences and performance, specifically focusing on task allocation and scheduling in collaborative settings. We present a proactive task allocation approach with three primary objectives: enhancing team performance, incorporating human preferences, and upholding a positive human perception of the robot and the collaborative experience. Through a user study, involving an autonomous mobile manipulator robot working alongside participants in a collaborative scenario, we confirm that the task planning framework successfully attains all three intended goals, thereby contributing to the advancement of adaptive task planning in human-robot collaboration. This paper mainly focuses on the first two objectives, and we discuss the third objective, participants' perception of the robot, tasks, and collaboration in a companion paper.