
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 of radius 2 are mutually tangent, three resting on the floor and the fourth resting on the others. A tetrahedron, each of whose vertices touches the surface of one of the balls, is constructed such that its vertices are at the points of tangency. What is the length of each edge of the tetrahedron?
A) $\frac{2\sqrt{61}}{3}$
B) $\frac{14}{3}$
C) $\frac{4\sqrt{3}}{3}$
D) $2\sqrt{3}$
E) $4\sqrt{3}$

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