Min of Sum of 3 Terms

Algebra Level pending

Let \( x > 0\) and \(y > 0 \), and let \(m\) be the minimum value of \( 4 x^2 + \frac{y}{2x} + \frac{4}{xy} \). Let \(a\) and \(b\) be the values of \(x\) and \(y\), respectively, that yield the minimum value \(m\). What is the value of \( m + ab ?\)

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