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$\large \begin{cases} a+b+c=16 \\ a^2+b^2+c^2=90 \\ a^3+b^3+c^3=532 \end{cases}$

If $a$, $b$ and $c$ satisfy the system of equations above, find $a^4+b^4+c^4$.

You may use a calculator at the end. So best of luck!

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