Every 3 seconds someone develops dementia worldwide.Brain-training exercises, preferably involving also physical activity, have shown their potential to monitor and improve the brain function of people affected by Alzheimer Disease (AD) or Mild Cognitive Impairment (MCI).This paper presents a cognitive robotic system designed to assist mild dementia patients during brain-training sessions of sorting tokens, an exercise inspired by the} Syndrom KurzTest neuropsychological test (SKT). The system is able to perceive, learn and adapt to the user’s behaviour and is composed of two main modules. The adaptive module based on representing the human-robot interaction as a planning problem, that can adapt to the user performance offering different encouragement and recommendation actions using both verbal and gesture communication in order to minimize the time spent to solve the exercise. As safety is a very important issue, the cognitive system is enriched with a safety module that monitors the possibility of physical contact and reacts accordingly. The cognitive system is presented as well as its embodiment in a real robot. Simulated experiments are performed to i) evaluate the adaptability of the system to different patient use-cases and ii) validate the coherence of the proposed safety module. A real experiment in the lab, with able users, is used as preliminary evaluation to validate the overall approach. Results in laboratory conditions show that the two presented modules effectively provide additional and essential functionalities to the system, although further work is necessary to guarantee robustness and timely response of the robot before testing it with patients.