Past research on action planning has shed light on the neural mechanisms underlying the selection of simple motor actions, along with the cognitive mechanisms underlying the planning of action sequences in constrained problem solving domains. We extend this research by describing a neural model that rapidly plans action sequences in relatively unconstrained domains by manipulating structured representations of objects and the actions they typically afford. We provide an analysis that indicates our model is able to reliably accomplish goals that require correctly performing a sequence of up to 5 actions in a simulated environment. We also provide an analysis of the scaling properties of our model with respect to the number of objects and affordances that constitute its knowledge of the environment. Using simplified simulations we find that our model is likely to function effectively while picking from 10,000 actions related to 25,000 objects.