The function $f$, defined on the set of ordered pairs of positive integers, satisfies the following properties: \begin{align*}  f(x,x) &=x, \\  f(x,y) &=f(y,x), \quad \text{and} \\ (x + y) f(x,y) &= yf(x,x + y).  \end{align*}Calculate $f(14,52)$.

Let's think step by step and output the final answer within \boxed{}.
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