An ellipse has the equation \(\frac{(x-2)^2}{25} + \frac{(y+3)^2}{9} = 1\). A parabola with its vertex at the center of the ellipse is given by the equation \(y = a(x-2)^2 - 3\). If one of the foci of the ellipse lies on the parabola, find the value of \(a\). Let's think step by step and output the final answer within \boxed{}.
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