\[ \large \begin{cases}{a+b+c=3} \\ {a^2 +b^2 +c^2 =5} \\ {a^3 + b^3 +c^3 = 7} \end{cases} \]

If \(a,b,c\) are complex numbers satisfying the system of equations above, find the value of \(a^4 + b^4 + c^4\).

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