
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 hexadecagon (16 sides) is inscribed in a circle with radius $r$ meters. Calculate the area of the hexadecagon in square meters.
A) $4r^2(\sqrt{2} - 1)$  
B) $4r^2(\sqrt{2} - \sqrt{2})$  
C) $4r^2(\sqrt{2} + \sqrt{2})$  
D) $4r^2 (\sqrt{2 - \sqrt{2}})$  
E) $3r^2\sqrt{3}$

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