
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
Through the center \( O \) of the circle circumscribed around the regular pentagon \( A B C D E \), lines parallel to the sides \( A B \) and \( B C \) are drawn. Their points of intersection with \( B C \) and \( C D \) are denoted as \( F \) and \( G \) respectively. What is the ratio of the areas of the quadrilateral \( O F C G \) and the pentagon \( A B C D E \)?

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