Garden Fan Palm
From my research on this tree it is a Fiji Fan Palm, Pritchardia pacifica. Contrary to it's name it originates in Tonga (officially the Kingdom of Tonga). Not sure how it got to the east side of Mexico from the middle of the Pacific Ocean.
The tree puts out a separate smaller limb that starts as a group of buds and eventually flowers out.
The flowers eventually turn into berries. As the berries ripen they change from green to yellow to red and then black where they eventually fall off. I have been told these berries are not edible which is a shame because there are always many bunches of berries on this tree in all various stages.
This tree is advertised as one of the most beautiful fan palms in existence, and there are hundreds of different varieties of fan palms. They tend to grow slow so it's difficult to find the trees themselves for sale (it's difficult to justify the investment of growing a tree 5 years and selling it at a price that people are willing to pay). I have found the seeds online to buy, or just come over and grab some off the ground if you want.
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