\[ \begin{cases} 2x^2 - 6xy + 2y^2 + 43 x + 43 y &=& 174, \\ x^2 + y^2 + 5x + 5y &=& 30 \end{cases} \]

The real numbers \(x \) and \( y \) satisfy the nonlinear system of equations above.

Find the largest possible value of \( |xy|\).

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