
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
Given a cube of side length 2 units, select four vertices such that they form a regular octahedron. Determine the ratio of the surface area of the cube to the surface area of the octahedron.
A) $3\sqrt{3}$
B) $2\sqrt{3}$
C) $\sqrt{6}$
D) $2\sqrt{2}$
E) $3\sqrt{2}$

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