
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
Paint each face of the cube ABCD-A<sub>1</sub>B<sub>1</sub>C<sub>1</sub>D<sub>1</sub> with different colors, ensuring that any two adjacent faces are not the same color. Now, there are 5 different colors available, and the colors of the 3 faces passing through vertex A have been painted. How many coloring schemes are there for the remaining 3 faces?

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