Sorry but forming hypothesis based on observations, which is what assumptions means to me, is induction. They are fallible so they need to be proven in order to be accepted. Usually that's done by proof of contradiction.

But you don't need to prove them to use them. Many people go around believing unproven theories. In the sciences the preference is for verified theories(and theorems in math) and we prove them by deduction.

But it seems that you know that. I don't understand why you don't like induction in a general algorithm. We don't have to restrict ourselves to a single type of reasoning. Induction, deduction, abduction are all valid and used by humans for generating new knowledge.

I might be misunderstanding something in which case please correct me.