
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
Andrew the Antelope canters along the surface of a regular icosahedron, which has twenty equilateral triangle faces and edge length 4.  If he wants to move from one vertex to the opposite vertex, the minimum distance he must travel can be expressed as  $\sqrt{n}$  for some integer  $n$ .  Compute  $n$ .

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