
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 and an equilateral triangle are such that the area of the equilateral triangle is double the area of the hexagon. What is the ratio of the perimeter of the triangle to the perimeter of the hexagon?
A) 2
B) 3
C) $\sqrt{6}$
D) $\sqrt{3}$
E) 6

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