The points $A$, $B$, $M$, and $N$ lie on a circle with center $O$. The radii $OA$ and $OB$ are perpendicular to each other. The line segment $MN$ is parallel to $AB$ and intersects the radius $OA$ at point $P$. Find the radius of the circle given that $|MP| = 12$ and $|PN| = 2\sqrt{14}$.

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