
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 identical balls, each of radius $2$, are positioned such that four balls are each mutually tangent on the floor and the fifth ball rests atop them in the gaps. A pyramid with a square base (square pyramid) is circumscribed around these balls. Calculate the edge length $s$ of the square base of the pyramid.
A) $4$
B) $8$
C) $4\sqrt{2}$
D) $8\sqrt{2}$
E) $16$

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