To suggest something softly, use Maybe you could or You might want to before a verb, or Have you considered before an -ing word. Perhaps makes any idea sound gentler.
Gentle suggestions
Maybe you could — Maybe you could go to bed earlier.
You might want to — You might want to try tea instead.
Have you considered — Have you considered taking a break?
Try it: Amina: I feel tired all the time. Hiroshi: ___ going to bed earlier? Choose the gentle suggestion that fits before the -ing word. (Have you considered / You'd better / You must) Answer: Have you considered — Have you considered is a gentle suggestion and fits before going. You'd better and You must are both stronger advice and are followed by a base verb, so neither one fits here.
Stronger advice
When the advice is important, use You'd better to warn of a problem, and You must for advice you feel strongly about.
You'd better — You'd better see a doctor.
You must — You must take care of yourself.
Try it: Sofia: The pain has not stopped for a week. Diego: ___ see a doctor. This is serious. Choose the strong advice for a serious problem. (You'd better / Maybe you could / Have you considered) Answer: You'd better — You'd better warns about a serious problem, which fits here. Maybe you could and Have you considered are both gentle suggestions, so neither one is strong enough for something serious.