\[\begin{align} (2-3i)z + (5+i)w &= 19-4i\\ (1-i)z + (2+i)w &= 9-i \end{align}\]

Let \(z\) and \(w\) be the complex numbers satisfying the equations above.

Compute \(|z+w|^2\).

\(\)

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

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