As people rely more and more on technology to solve problems, the ability of humans to think for themselves will surely deteriorate.
Discuss the extent to which you agree or disagree with the statement and explain your reasoning for the position you take. In developing and supporting your position, you should consider ways in which the statement might or might not hold true and explain how these considerations shape your position.
What if I use ‘reason’ instead of ‘reasoning’?
You would rather say “the reason for the position you take” than “your reason for the position you take” here, so it would sound less idiomatic. But apart from that, I’d say you normally don’t have a reason “for” a position: you can have a reason “to take a position”, but “a reason for a position” sounds less appropriate somehow in this context. Thirdly, and most importantly, the assignment asks about the process or argumentation that led you to this position, not a single reason/argument; hence “reasoning” is better.