The limiting case or the simplest form of induction is the example. Even by only one example we may already begin to deduce. Hence induction depends on the example, and deduction depends also on the example, which it uses by circularly reproducing it into a conclusion. – Hence nothing must be accepted or be taken for granted, it is quite easy, if you just let me explain it without a highbrow style.
If we add to the above example in comparison a second one, the analogy is born, and hence analogy is analogous to induction, since we just take not one example but another one in association.
By reversing the deduction we arrive at abduction or criminal cause.
So, there is no necessity to doubt the validity of induction and deduction because they are so well embedded into example, analogy and cause.
(P.S.: The circular, deductive reproduction of the example into a conclusion is already an analogy, because it is its utilization to a further event that occurs after the first example. – But I have omitted this in the answer, as a little riddle.)