\begin{aligned} a \ \ + b \ + c \ \ &=& 2\\ a^{ 2 } + b^{ 2 } + c^{ 2 } &=& 6\\ a^{ 3 } + b^{ 3 } + c^{ 3 }&=& 8\\ \end{aligned} For complex numbers $a,b,c$, we are given the system of equations above. Find the value of $a^{ 4 } + b^{ 4 } + c^{ 4 }$.