This is more of a comment than an answer. In fact it's more of an advice.
Higher-order thinking and inductive reasoning have rather vague definitions, in my mind. They seem to also come from different backgrounds. If you don't mind, I think it's easier to approach your situation rather than your question. You might find it refreshing to think of higher-order thinking as a phenomena that occurs under certain conditions; in addition to thinking of it as a muscle (which is implied by your question). Specifically, if you look at higher-order thinking, as you call it, as a state to be entered into, some of the greater facilitators are ability to relax and to change perspectives effectively with emphasis on relaxation. This is within the scope of neurolinguistics, if you'd prefer a contemporary approach; if you don't mind going old school with this, more or less any meditation, should lead to noticeable improvements or autogenic training might float your boat.
I hope this is helpful. I regret not providing any references. Edits are welcome.