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

Note: I found the problem in my Book. See: "Ayo Raih Medali Emas Olimpiade Matematika" (English: Let's Get A Gold Medal in Mathematics Olympiad) by: Dr. Khow Yao Tung, M. Sc. Ed, MEd.

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