Goffin's cockatoos (Cacatua goffiniana) can solve a diverse set of mechanical problems, such as tool use, tool manufacture, and mechanical puzzles. However, the proximate mechanisms underlying this adaptive behavior are largely unknown. Similarly, engineering artificial agents that can as flexibly solve such mechanical puzzles is still a substantial challenge in areas such as robotics. This article is an interdisciplinary approach to study mechanical problem solving which we hope is relevant to both fields. The behavior we are studying results from the interaction between a complex environment (the lockbox) and different processes that govern the animals' behavior. We therefore jointly analyze the parrots' (1) engagement, (2) sensorimotor skill learning, and (3) action selection. We find that none of these aspects could solely explain the animals' behavioral adaptation and that a plausible model of proximate mechanisms must jointly address these aspects. We accompany this analysis with a discussion of methods to identify such mechanisms. At the same time, we argue, it is implausible to identify a detailed model from the limited behavioral data of just a few studies. Instead, we advocate for an incremental approach to model building in which one first establishes constraints on proximate mechanisms before specific, detailed models are formulated. To illustrate this idea, we apply it to the data presented here. We argue that as the field attempts to find mechanistic explanations for increasingly complex behaviors, such alternative modeling approaches will be necessary.