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「今日は何する?」

I found this sentence by a Japanese person on a Japanese speaking website. I am aware that の is the possessive particle in Japanese, and allows for sentences such as

「僕娘は店に行って靴を買います。」

But what I don't understand is why の is used at the end of the first sentence without directly stating anything. Why exactly is の being used like that, and what does it mean?