Let $A$, $B$, and $C$ be three points on the edge of a circular chord such that $B$ is due west of $C$ and $\triangle ABC$ is an equilateral triangle with each side measuring $86$ meters. A boy swam from $A$ directly towards $B$. After covering a distance of $x$ meters, he turned and swam westward, reaching the shore after covering a distance of $y$ meters. If $x$ and $y$ are both positive integers, determine $y$.

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