Apply Vieta's?

Algebra Level 5

\[\large{\begin{cases} a+b+c = 0 \\ a^{2}+b^{2}+c^{2} = 1 \end{cases} }\]

Let \(a,b,c\) be real numbers satisfying the above system of equations. Find the maximum possible value of \((9abc)^2\).

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