
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
Five balls of radius $2$ are tangent to each other in such a way that four balls are resting on the floor, forming a square, and the fifth ball is resting on top of these four. A tetrahedron, each of whose edges have length $s$, is circumscribed around the upper ball and any three of the bottom balls. Find $s$.
A) $2\sqrt{6}$
B) $4\sqrt{2}$
C) $4$
D) $8$
E) $6$

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