Computational cognitive architectures are broadly scoped models of the human mind that combine different psychological functionalities (as well as often different computational methods for these different functionalities) into one unified framework. They structure them in a psychologically plausible and validated way. However, such models thus far have only limited computational capabilities, mostly limited by the computational tools and techniques that were adopted. More recently, LLMs have proved to be more capable computationally than any other tools. Thus, in order to deal with both real-world complexity and psychological realism at the same time, incorporating LLMs into cognitive architectures naturally becomes an important task. In the present article, a synergistic combination of the Clarion cognitive architecture and LLMs is discussed as a case study. The implicit-explicit dichotomy that is fundamental to Clarion is leveraged for a seamless integration of Clarion and LLMs. As a result, computational power of LLMs is combined with psychological nicety of Clarion.