Your strategy is similar to mine, except that I only focus on the types.

Which types are required to define the function, both as parameters and through any global/inherited scope/other state? Which types are directly related, eg, containers to string, containers themselves, indexing, etc?

By the time you have some sense of what things go where in the program, and what they turn in to, you usually have significantly narrowed down what the program can be doing.

Note: This works considerably better with some languages than others, but can work reasonably well on weakly typed things like Python.