
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
In the diagram, an equilateral hexagon $ABCDEF$ has four nonadjacent acute interior angles that each measure $45^\circ$. The enclosed area of the hexagon is $12\sqrt{2}$. What is the perimeter of the hexagon?
A) $4\sqrt{6}$
B) $6\sqrt{6}$
C) $12$
D) $12\sqrt{3}$
E) $18\sqrt{2}$

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