
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
On a cubic planet, cubic mice live only on the faces of the cube and not on the edges or vertices. The number of mice on different faces is different and on any two neighboring faces, this number differs by at least 2. What is the minimum number of cubic mice that can live on this planet if there is at least one mouse on each face?

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