
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 circle is inscribed in a regular hexagon. A smaller hexagon has two non-adjacent sides coinciding with the sides of the larger hexagon and the remaining vertices touching the circle. What percentage of the area of the larger hexagon is the area of the smaller hexagon? Assume the side of the larger hexagon is twice the radius of the circle.

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