This chapter presents the first contribution to the adaptive pillar by introducing an adaptive Robot-Assisted Cognitive Training (RACT) system based on high-level symbolic task planning. The proposed system formalises human-robot interactions as a planning problem whose objective is to find, given the current state, the robot’s socially assistive behaviour that best suits the user’s needs. Initially, the feasibility of the RACT system is investigated through simulation and a preliminary pilot study involving a limited number of participants. Subsequently, empirical findings from an experiment involving N=24 untrained participants in a real-world setting are presented to gauge the efficacy of the robot’s adaptive behaviour on users’ performance. The chapter concludes by highlighting the feasibility of the proposed methodology and the robot’s ability to adjust its assistance based on a limited number of interactions.