
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 hexagon $ABCDEF$. The first circle is tangent to $\overline{AB}$ and the second circle is tangent to $\overline{DE}$. Both circles are tangent to lines $BC$ and $FA$. If the radius of the first circle is $2$, and the radius of the second circle is $3$ times that of the first, find the ratio of the area of the second circle to that of the first circle.

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