
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 is inscribed in a circle. The length of each side of the hexagon is 6 units. Calculate:
1. The radius of the circumscribed circle.
2. The total circumference of the circle.
3. The arc length corresponding to one side of the hexagon.
4. The area of the hexagon.
A) Radius: 6 units, Circumference: \(12\pi\) units, Arc length: \(2\pi\) units, Area: \(54\sqrt{3}\) square units
B) Radius: 3 units, Circumference: \(6\pi\) units, Arc length: \(\pi\) units, Area: \(13.5\sqrt{3}\) square units
C) Radius: 12 units, Circumference: \(24\pi\) units, Arc length: \(4\pi\) units, Area: \(216\sqrt{3}\) square units
D) Radius: 9 units, Circumference: \(18\pi\) units, Arc length: \(3\pi\) units, Area: \(121.5\sqrt{3}\) square units

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