
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
Two circles lie outside a regular octagon $ABCDEFGH$. Both circles are tangent to lines $AB$ and $CD$. The first circle is also tangent to line $BC$, and the second circle is also tangent to line $DE$. What is the ratio of the area of the second circle to that of the first circle?
A) 2
B) 3
C) 4
D) 5
E) 6

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