
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 cut by a plane parallel to two of its opposite faces. The plane intersects the octahedron such that the cross-section formed is a square. Find the area of this square expressed in simplest form 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) \( \frac{2\sqrt{3}}{4} \)
B) \( \frac{3\sqrt{3}}{4} \)
C) \( \frac{3}{4} \)
D) \( \frac{3\sqrt{3}}{8} \)
E) \( \frac{3\sqrt{2}}{4} \)

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