Not too reduced

Determine the smallest positive integer \(n\) such that \(17n + 12 = x \times z \) and \( n - 25 = y \times z \), where \(x, y, \mbox{ and } z\) are positive integers, \(x\) and \(y\) are coprime, and both \(y\) and \(z\) are strictly greater than \(1.\)

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