
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 $s$. A plane that is parallel to two of its opposite faces and exactly one-third distance from the top vertex to the bottom vertex cuts the octahedron. Determine the area of the polygon that is the intersection of the plane and the octahedron.
A) $\frac{\sqrt{3}s^2}{8}$  
B) $\frac{\sqrt{3}s^2}{6}$  
C) $\frac{\sqrt{3}s^2}{4}$  
D) $\frac{\sqrt{3}s^2}{3}$  
E) $\frac{\sqrt{3}s^2}{12}$

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