The Novamente Cognition Engine (NCE) architecture for Artificial General Intelligence is briefly reviewed, with a focus on exploring how the various cognitive processes involved in the architecture are intended to cooperate in carrying out moderately complex tasks involving controlling an agent embodied in the AGI-Sim 3D simulation world. A handful of previous conference papers have reviewed the overall architecture of the NCE, and discussed some accomplishments of the current, as yet incomplete version of the system; this paper is more speculative and focuses on the intended behaviors of the NCE once the implementation of all its major cognitive processes is complete. The “iterated Easter Egg Hunt” scenario is introduced and used as a running example throughout, due to its combination of perceptual, physical-action, social and self-modeling aspects. To aid in explaining the intended behavior of the NCE, a systematic typology of NCE cognitive processes is introduced. Cognitive processes are typologized as global, operational or focused; and, the focused processes are more specifically categorized as either forward-synthesis or backward-synthesis processes. The typical dynamics of focused cognition is then modeled as an ongoing oscillation between forward and backward synthesis processes, with critical emergent structures such as self and consciousness arising as attractors of this oscillatory dynamic. The emergence of models of self and others from this oscillatory dynamic is reviewed, along with other aspects of cognitive-process integration in the NCE, in the context of the iterated Easter Egg Hunt scenario.