An entirely novel synthesis combines the applied cognitive psychology of a task analytic approach with a neural cell assembly perspective that models both brain and mind function during task performance; similar cell assemblies could be implemented as an artificially intelligent neural network. A simplified cell assembly model is introduced and this leads to several new representational formats that, in combination, are demonstrated as suitable for analysing tasks. The advantages of using neural models are exposed and compared with previous research that has used symbolic artificial intelligence production systems, which make no attempt to model neurophysiology. For cognitive scientists, the approach provides an easy and practical introduction to thinking about brains, minds and artificial intelligence in terms of cell assemblies. In the future, subsequent developments have the potential to lead to a new, general theory of psychology and neurophysiology, supported by cell assembly based artificial intelligences.