I've always considered induction to be the most important part of reasoning. Without induction, it is impossible to actually have a premise in way except the most hypothetical. While I enjoy coming up with unsupported premises and seeing where they go deductively, they are not at all useful if you can't figure out at some point what is actually the case. An argument is only sound if it is valid and the premises are true. Induction allows you to actually stop at some point and say which premises are true.

Occam's razor is an example of a good inductive tool. It isn't strictly correct, but it works pretty well. I agree strongly with the idea that you use the best of your current capability to determine how to improve. You just have to hope you are starting at a good enough position that it ends up going in the right direction.