
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 each of radius 2 are arranged such that four balls are mutually tangent to each other on a flat surface, and a fifth ball is placed on top and tangent to these four. A tetrahedron is circumscribed around this arrangement of balls. Calculate the edge length \( s \) of this tetrahedron.
A) \( 4\sqrt{2} \)
B) \( 2\sqrt{5} \)
C) \( 4\sqrt{5} \)
D) \( 8 \)
E) \( 5\sqrt{2} \)

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