Here are my notes about making it more clear

A "command" 0<=cmd<=UINT_MAX is obfuscatedly associated with one of 5 functions f_A(x)
where 'A' (the "action") is the function's label and takes the values 0<=A<=4

After training you should be able to undo the obfuscation
to determine which action (which function f_A) is referred to by cmd

The function get_action(action)(x) evaluates the function f_action(x).
In order to determine if you have the correct function picked out,
you have to guess an action 'a', calculate sample outputs y=f_a(x) using command(cmd, x),
and using response(y==Y) you can update your guess of 'a' depending on whether or not
the output y corresponds with the true output Y=f_A(x) for all inputs x