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It makes sense from a boolean perspective. E.g "I'll try and go to the store." If the try fails, you did not go to the store.

Only if your language has short-circuiting booleans.

That’s just the meaning of “try” tho; “I’ll try to go to the store” is identical in meaning

For that matter, "trying" is implied by "going", and you could just say "I'll go to the store".

Nah, there's a markèd difference in the expressed certainty there