Not AM-GM

Algebra Level 4

Find the maximum value of \[\ \frac { a }{ c } + \frac { b }{ d } + \frac { c }{ a } + \frac { d }{ b }, \] where \(a,b,c,d\) vary over all distinct real numbers such that \( \frac { a }{ b } + \frac { b }{ c } + \frac { c }{ d } + \frac { d }{ a } = 4\) and \(ac = bd\).

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