The function $f$, defined on the set of ordered pairs of positive integers, satisfies the following properties:
\[f(x, x) = x,\; f(x, y) = f(y, x), {\rm \ and\ } (x+y)f(x, y) = yf(x, x+y).\]
Calculate $f(14,52)$.


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