Answer: Filicium decipiens, the Japanese Fern tree, is a beautiful evergreen with moderate growth rate. The canopy will eventually become 30' in diameter which may be a little large for the planting site unless you keep it pruned. The roots of this tree are not especially invasive but they will travel out nearly two times the diameter of the canopy.
I'd tend to plant something with less litter - Giant Bird of Paradise, or banana tree for instance. The foliage is soft and won't pose a hazard to anyone near the pool.
Best wishes with your landscape!
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