Forget about the term "particle". Learn pragmatic grammar for now. As you say out is an adverb in "put out", which means "out" is "unnecessary" in a sense. I can figure it out. I can figure out it. The "out" is to modify the verb "figure", "put", etc, as an adverb, it is with the verb. Remember that. Adverbs work for verbs, not for the objects (noun), in this case, "it". On the contrary, a preposition is a connector connecting an intransitive verb and the object. Since the verb is not "transitive", it needs a helper to help it to transfer, that is, a preposition. That is, why you can't change the position of the preposition in the sentence, but can only put it between the verb and the object.