Personalized adaptive interventions offer the opportunity to increase patient benefits, however, there are challenges in their planning and implementation. Once implemented, it is an important question whether personalized adaptive interventions are indeed clinically more effective compared to a fixed gold standard intervention. In this paper, we present an innovative N-of-1 trial study design testing whether implementing a personalized intervention by an online reinforcement learning agent is feasible and effective. Throughout, we use a new study on physical exercise recommendations to reduce pain in endometriosis for illustration. We describe the design of a contextual bandit recommendation agent and evaluate the agent in simulation studies. The results show that adaptive interventions add complexity to the design and implementation process, but have the potential to improve patients' benefits even if only few observations are available. In order to quantify the expected benefit, data from previous interventional studies is required. We expect our approach to be transferable to other interventions and clinical interventions.