
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 through the octahedron, but not symmetrically at the midpoint, instead at three-quarters of the height from the base to the opposite vertex of each face. Determine the area of the polygon formed by the intersection of the plane and the octahedron. Express your answer in the form  \frac{a\sqrt{b}}{c} , where  a ,  b , and  c  are positive integers,  a  and  c  are coprime, and  b  is not divisible by the square of any prime. Calculate  a  +  b  +  c .

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