
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 octagon $ABCDEFGH$, and $Y$ is a point dividing the side $\overline{BC}$ in the ratio 1:3 (from B to C). What fraction of the area of the octagon is shaded?
A) $\frac{15}{32}$
B) $\frac{16}{32}$
C) $\frac{17}{32}$
D) $\frac{18}{32}$
E) $\frac{19}{32}$

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