Complex Egyptian Fractions

\[\dfrac{5}{4-3i} = \dfrac{1}{v} + \dfrac{1}{w} + \dfrac{1}{z}\]

Let \(v,w,z\) be the Gaussian integers, satisfying the equations above, where \(1< |v| < |w| < |z|\) and \(v+w+z\) is real.

What is the least possible value of \(|v|^2 + |w|^2 + |z|^2\)?

Note: \(i^2 = -1\), and \(|z|\) is the absolute value of \(z\).

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