
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Point $O$ is the center of the regular hexadecagon $ABCDEFGHIJKLMNOP$, and $X$ is the midpoint of the side $\overline{AB}$. Let $Y$ be the midpoint of the segment $\overline{AX}$. What fraction of the area of the hexadecagon is shaded, where the shaded region is bound by segments $\overline{OY}$, $\overline{YB}$, and arc $BCDEFGHIA$?

Present the answer in LaTex format: \boxed{Your answer}
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