The problem with adding definitions to words like “thinking” and “free will” is that doing so means humans can no longer pretend they are special.
Even in this thread, the number of people claiming some mystical power separating humans from all the rest of nature is quite noticeable.
This exact argument applies to "free will", and that definition has been debated for millennia. I'm not saying don't try, but I am saying that it's probably a fuzzy concept for a good reason, and treating it as merely a behavioural descriptor for any black box that features intelligence and unpredictable complexity is practical and useful too.