
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 square and a regular octagon have equal perimeters. If the area of the square is 16, what is the area of the octagon?
A) $8 + 4\sqrt{2}$
B) $4 + 2\sqrt{2}$
C) $16 + 8\sqrt{2}$
D) $4\sqrt{2}$
E) $8\sqrt{2}$

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