
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 decagon $ABCDEFGHIJ$, and $X$ is the midpoint of the side $\overline{AB}.$ What fraction of the area of the decagon is shaded if the shaded region includes the triangles $\triangle CFO$, $\triangle DFO$, $\triangle EFO$, and half of $\triangle BFO$?
A) $\frac{3}{10}$ 
B) $\frac{7}{20}$ 
C) $\frac{9}{40}$ 
D) $\frac{1}{4}$ 
E) $\frac{11}{20}$

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