
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 with side length $2$ is intersected by a plane parallel to two of its opposite faces. This plane divides the octahedron into two congruent solids. Determine the area of the polygon formed by the intersection of the plane and the octahedron. Express the area as $\frac{a\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers with $a$ and $c$ relatively prime, and $b$ not divisible by the square of any prime.
A) 16
B) 18
C) 20
D) 22
E) 24

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