As the worldwide population gets increasingly aged, in-home tele-medicine and mobile-health solutions represent promising services to promote active and independent aging and to contribute to a paradigm shift towards a patient-centric healthcare. In this work, we present ACTA (Advanced Cognitive Training for Aging), a prototypal mobile-health solution to provide advanced cognitive training for senior citizens with mild cognitive impairments, We disclose here the conceptualization of ACTA as the integration of two promising rehabilitation strategies: the "Nudge theory", from the cognitive domain, and the neurofeedback, from the neuroscience domain. Moreover, in ACTA we exploit the most advanced machine learning techniques to deliver customized and fully adaptive support to the elderly, while training in an ecological environment. ACTA represents the next-step beyond SENIOR, an earlier mobile-health project for cognitive training based on Nudge theory, currently ongoing in Lombardy Region. Beyond SENIOR, ACTA represents a highly-usable, accessible, low-cost, new-generation mobile-health solution to promote independent aging and effective motor-cognitive training support, while empowering the elderly in their own aging.