What's the difference between the endings "ou to suru" and "- te miru" in japanese when trying to do somethin?

I mean, what''s the difference between saying しようとする and してみる??? Is there any difference? Can you explain it to me? 分かる為にこの和文を直してくれて下さい。 (Please correct this japanese sentence so I can understand). What I want to say: "I've never exchanged letters before but I'm trying to write a... show more I mean, what''s the difference between saying しようとする and してみる???
Is there any difference? Can you explain it to me?

分かる為にこの和文を直してくれて下さい。
(Please correct this japanese sentence so I can understand).

What I want to say: "I've never exchanged letters before but I'm trying to write a letter for a japanese friend who lives in tokyo".

文通をしたことないのに東京に住んでる日本人の友のため
手紙を書こうとしてる。

Should I say 書こうとしてる or 書いてみてる??

Please help me.

Thanks.
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