
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 an octahedron floating in space oriented such that one face is vertical at the top and the opposing face is vertical at the bottom. Each face of the octahedron is an equilateral triangle, and the octahedron features 8 faces. Moving from the top to the bottom vertex, via a sequence of adjacent faces, count the number of ways each face can be visited exactly once and without moving back to the previously visited face.
A) 36
B) 48
C) 72
D) 96
E) 120

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