It's obvious that its is a possessive pronoun.
It's is a contraction for it is or it has.
Its is a possessive pronoun meaning, more or less, of it or belonging to it.
And there is absolutely, positively, no such word as its'.
A simple test
If you can replace it[']s in your sentence with it is or it has, then your word is it's; otherwise, your word is its.
Its is the neuter version of his and her. Try plugging her into your sentence where you think its belongs. (It's better to use her for reasons I may explain someday.) If the sentence still works grammatically (if not logically) then your word is indeed its.