
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
Consider a regular icosahedron (a polyhedron with 20 triangular faces), floating in space with one vertex pointing directly up and one directly down. The icosahedron has three horizontal rings: the top ring (right below the top vertex), a middle ring, and a bottom ring (just above the bottom vertex). How many ways are there to traverse from a triangle in the top ring to a triangle in the bottom ring via adjacent faces, visiting each face at most once, without moving upwards from any subsequent lower ring once descended?
A) 100
B) 200
C) 300
D) 400
E) 500

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