\[ \begin{equation} \left\{ \begin{aligned} a+b+c=0\\ abc=2\\ \end{aligned} \right. \end{equation}\]

Let \(a,b\) and \(c\) be real numbers satisfying the system of equations above. Minimize \[|a|^{3}+|b|^{3}+|c|^{3}.\]

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