Induction and deduction are foundational to human rationality because it is impossible for a human to stop using them. Indeed what it means to be humanly rational is that one uses these reasoning systems.
There is no sense in trying to discover any justification for these two reasoning systems because even if we discovered that one of them ought not to be used, then we could not stop using them. If we cannot stop using them even if we ought to, then it is futile, indeed a waste of time, to examine if we ought not to use them.
Those who think that ought implies can might also reason like this: If we cannot stop using them, then it is not the case that we ought not to use them. This follows from the contra-position of the proposition ‘ought implies can’, that is, ‘cannot implies ought not’. If it is not the case that we ought not to use them, then they are justified. This follows from the contra-position of the proposition if we are not justified in using a reasoning system, then we ought not to use it, that is, ‘if it is not the case that we ought not to use a reasoning system, then we are justified in using that reasoning system’. Therefore, we are justified in using induction and deduction. Reasoning like this eliminates the arbitrariness of “choosing” these two reasoning systems. There are no other reasoning systems that we cannot stop using if we wanted to.
Note that the foregoing reasoning uses deduction. I’m not sure if that is a problem. It may be.