
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
Four balls, each of radius $2$, are mutually tangent. One ball rests on a platform of height $2$, and three balls rest on the floor, with each of these three touching the elevated ball. A tetrahedron, each of whose edges have length $s$, is circumscribed around these balls. What is $s$?
A) $4\sqrt{3}$
B) $8$
C) $\frac{8\sqrt{3}}{3}$
D) $\frac{2\sqrt{3}}{3}$
E) $12$

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