I realized a while ago (and am finally getting around to writing about it) that fan fiction and poetry are actually pretty similar. And I mean beyond the fact that girls in high school friggin' love them.
Fan fiction and poetry both make use of commonly known things. In fanfic, it is characters, objects, and relationships. In poetry, it is feelings and symbols. Nobody needs a sunset explained to them, nor do they need to know the relationship between Spock and Kirk. As such, we can progress further much sooner because of not having to establish those things.
They can also both be very dense. This comes from that shared understanding. Characters in fanfic do not need to go into soliloquy or extended monologue/dialogue about how they feel or why they did the things they did. In poetry, we are writing on several levels, usually the literal level of the scene, as well as the metaphorical level of the symbolic meaning of the components of the scene.
To that end, poetry and fan fiction also share the quality of being exceptionally difficult to do well. The ability to have well-known characters not break their canon or betray their personalities, to have them speak the way they should sound, and all while having an interesting and relevant story is hard. So is writing a poem that can simultaneously show an interesting scene at face value, but also have that scene, elicit powerful thoughts and emotions in the blink of an eye. That is also why the vast majority of both fanfic and poetry are trash, liked only by the person who wrote it (and not always then), and make the minute percentage of truly excellent works in the fields completely ignored.
You can probably guess my advice by now. (Give it a shot already.)