
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 spheres, each of radius $2$, are packed such that four of them are placed at the vertices of a horizontal square and the fifth sphere is placed exactly above the center of the square, touching all four spheres below. A regular tetrahedron is to be constructed around these spheres so that each vertex of the tetrahedron is at the center of one of the spheres (excluding the center sphere), with one edge extending directly upwards to the center of the top sphere. Calculate the edge length $s$ of this tetrahedron.
A) $2\sqrt{6}$
B) $4\sqrt{3}$
C) $4\sqrt{2}$
D) $6$
E) $8$

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