The evolution from the Edge-Cloud Continuum to the Cognitive Computing Continuum (CCC) has introduced new challenges which necessitate advanced frameworks that integrate cognitive capabilities to enhance interoperability, adaptability, and resource efficiency. Considering insights from ongoing research and initiatives on the cognitive cloud, we identify the core concepts essential for transitioning to the CCC, including cognitive orchestration, distributed AI, and sovereign data management. We then introduce ENACT, a novel framework designed to embrace these concepts aiming to provide cognitive, highly adaptive orchestration to support modern hyper-distributed and data-intensive applications. Furthermore, ENACT employs bespoke mechanisms to enable dynamic continuum modelling and visibility as well as to facilitate application-level automation and adaptability. This paper presents the motivation behind the ENACT approach, reviews the state-of-the-art across its fundamental technological concepts and highlights its key innovations. Overall, it contributes to the formalization of the CCC architectural principles and, ultimately, to the realization of CCC.