
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 icosahedron has a side length of $2$. A plane parallel to one of its faces cuts through the middle of the icosahedron, creating an intersection that forms a hexagon. Determine the area of this hexagon.
A) $3\sqrt{3}$
B) $12\sqrt{3}$
C) $6\sqrt{3}$
D) $4\sqrt{3}$
E) $9\sqrt{3}$

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