
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 octahedron has side length 2. A plane parallel to two of its opposite faces cuts the octahedron one-third of the way from the base to the top, forming an intersection that has the shape of a regular polygon. Determine the area of this polygon in the form $\frac{a\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, $a$ and $c$ are relatively prime, and $b$ is not divisible by the square of any prime.
A) $\frac{8\sqrt{3}}{3}$
B) $\frac{7\sqrt{3}}{2}$
C) $\frac{9\sqrt{3}}{4}$
D) $\frac{10\sqrt{3}}{5}$
E) $\frac{11\sqrt{3}}{6}$

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