\[ \begin{eqnarray} a+b+c & = & 0 \\ a^2 + b^2 + c^2 & = & \sqrt{74} \\ \end{eqnarray} \]

Real numbers \(a,b,c\) satisfy the above equations.

What is the value of \(a^4 + b^4 + c^4\)?

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