This article begins with a comparison of two groups of teachers, working on the same tasks in Analytic Geometry. One group has only basic experience in CAS-assisted problem solving, and the other group has extensive experience. The comparison is discussed in terms of the interplay between reflection, operative knowledge and execution. The findings indicate that because of the different levels of their respective CAS-based operative knowledge, the first group outsourced traditional techniques and the more experienced teachers developed new instrumented techniques. By doing so, the second group uncovered routes to a lateral exploration of the problem. Following Chevallard's anthropological approach, we propose initial elements of a new praxeology, comprising tasks in the specific topic, instrumented techniques, technological discourse, and new mathematical perspectives.