Switchable Valued Function

Algebra Level 3

\(f\) is defined in \(\mathbb{Z^+}\) such that
\[ f(x,x) = x \\ f(x,y) = f(y,x) \\ (x+y)f(x,y) = yf(x,x+y). \\ \]

Find the value of \(f(14,52)\).

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