
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
Eight vertices of the cube \(A B C D - A_{1} B_{1} C_{1} D_{1}\) are to be colored with four different colors such that the endpoints of each edge have different colors. How many ways are there to color the cube?

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