
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 hexagon $ABCDEF$ with side length 2 is given. Two circles are positioned outside the hexagon. The first circle is tangent to line $\overline{AB}$ and the second circle is tangent to line $\overline{CD}$. Both circles are tangent to line $\overline{EF}$. Determine the ratio of the area of the second circle to the first circle.

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