Dependent progression

Let \(a\) and \(b\) be positive integers. Given that

  • \(a,x,y,z,b\) follows an arithmetic progression if \(x \cdot y \cdot z = 55 \).

  • \(a,x,y,z,b\) follows a harmonic progression if \(x \cdot y \cdot z = \frac{343}{55} \).

Find the value of \(a^2 + b^2 \).

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