Let \(a,b\) and \(c\) follows an arithmetic progression.

Denote \(x\) as the geometric mean of \(a\) and \(b\), and

denote \(y\) as the geometric mean of \(b\) and \(c\).

Find the arithmetic mean of \(x^2 \) and \(y^2\) in terms of \(a,b\) and/or \(c\).

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