
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 closed curve is composed of 12 congruent circular arcs, where each arc has a length of \(\frac{3\pi}{4}\), and the centers of these circles are located at the vertices of a regular octagon of side length 3 units. Calculate the area enclosed by this curve.
A) \(18 + \frac{81\pi}{8}\)
B) \(18\sqrt{2} + \frac{81\pi}{8}\)
C) \(9\sqrt{2} + \frac{81\pi}{4}\)
D) \(18(1 + \sqrt{2}) + \frac{81\pi}{8}\) 
E) \(36 + \frac{81\pi}{8}\)

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