
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 cube has a side length of 2 units. Four of its vertices form a regular tetrahedron. Those vertices are at positions (0,0,0), (2,2,0), (2,0,2), and (0,2,2). Determine the ratio of the surface area of the cube to the surface area of the tetrahedron.
A) $\sqrt{2}$   
B) $\sqrt{3}$   
C) $\sqrt{6}$   
D) $2\sqrt{3}$   
E) $4$

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