Haiji-sama
This is Kawaguchi Hidetoshi. This is my humble answer to the question.
Similar to Mr. Mitsumi, I think we should avoid easily saying “do your best” as much as possible, even from the experience of dealing with people with mental illness as the chairman of a social welfare corporation.
This “do your best”... when you look it up, it seems that there are two dominant etymologies of “work hard,” one is “dazzling,” and the other is “stick to yourself.”
“Being alert” means keeping an eye on it, looking closely, keeping an eye on it, not moving, and working without moving, etc.
“Struggling with oneself” means passing oneself through, staying in a fixed place, thing, or thing and not moving at all, etc.
In view of the above two, it seems that what is currently used as “making an effort” is derived from “continuing to work without getting bogged down.”
After a long period of ascetic practice, Buddha also finally sat under the Bodhi tree, worked on meditation without being moved (immobile) and was unfazed by attacks by numerous monsters (troublemakers), and eventually attained enlightenment.
Certainly, in order to achieve one thing, it is important to “keep working on it without getting fazed.” If you're half-hearted around here and there, there are times when you can't learn it, you won't be useful, and you won't be able to gain trust.
However, as Mr. Urakami said, this will also be “case by case.”
That is why there are many adverse effects if you “put your own mind” too much, get caught up, and get too attached.
Also, even if each individual wants to do their best, there are many cases where they cannot do their best. If you really think about that person and want to support, cooperate, or help, I don't just irresponsibly say “go for it, go for it,” but I also know that it is necessary to add friendly specific advice on how to do this and show it with actual visible actions (help/volunteer/service/labor provision, donation, etc.).
Kawaguchi Hidetoshi Gassho