A nice big hunk of sharpened steel, or failing that, a container that could be heated/reheated indefinitely.
I'll assume your reef is something nice and big, at least some 20-30 yards thick around the island to make it nearly impossible to break through with one person, which should give us plenty of space for spear fishing without depleting the reefs. A nice hunk of steel would allow me to carve out some bowls, or cut down a few trees to use for fires, construction material. Knowing that there's plants growing on the island tells me that there's some kind of aquifer on the island, since the plants would need some source of water in order to survive. Assuming I had enough food and water in the short term to dig the distance down, as in a few weeks worth of supplies, you could set up your own brackish water spring which will keep you alive, although it won't taste good. With water, protein, dried seaweed/plants, shelter, and a stockpile of other supplies, you could start building a small canoe to go float around the island, and if you get really bored, carve a small channel in the reef in order to eventually escape. This all assumes that the trees are of a decent size that need a good supply of water, if they're desert plants or adapted in some other way to last on the island with low rainfall you'd most likely lose the aquifer, but could use the plants themselves as a source of water since they'd have natural filters to remove the salt from the salt water.
But what do islanders know?