Birthday Problem!

Algebra Level 5

\[\large \displaystyle f(x+y) \leqslant yf(x)+f(f(x)) \]

Let \(f:\mathbb{R} \rightarrow \mathbb{R} \) be a real-valued function defined as shown above for all real numbers \(x\) and \(y\). Find \(\displaystyle f(-5699) \).

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