
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
A regular octagon $ABCDEFGH$ with a side length of 2 units has two circles placed externally. The first circle is tangent to side $AB$ at a single point and the second circle is tangent to side $EF$. Both circles are tangent externally to a line that passes through points $C$ and $G$. Find the ratio of the area of the first circle to that of the second circle.
A) 0.5
B) 1
C) 1.5
D) 2
E) 2.5

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