Re: to assess I think you're right.
This is only my impression, and others may disagree; but if a native speaker were to tell me that he tried to assess his health every now and then, it would sound perhaps a bit odd, as if he were over-concerned about his health.
For normal usage, you might simply say "I like to keep an eye on my health".
All the best,
MrP
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Not a professional ESL teacher.
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