
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
The toy factory produces wireframe cubes, with small multicolored balls placed at the vertices. According to the standard, each cube must use balls of all eight colors (white and the seven colors of the rainbow). How many different models of cubes can the factory produce?

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