
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 a side length of \(2\). A plane parallel to two of its opposite faces cuts the octahedron into two congruent solids. Find the area of the polygon formed by the intersection of the plane and the octahedron.

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