System of equations?

Algebra Level 3

\[ \large{ \begin{cases} y+4 = (x-2)^2 \\ x+ 4 = (y-2)^2 \end{cases} } \]

Let \(x\) and \(y\) be distinct numbers satisfying the system of equations above.

What is the value of \(x^2 + y^2\)?

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