
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
Mônica has six colors to paint the faces of a cube. How many ways can she do this if:

a) All faces are the same color?

b) Five faces are the same color and one face has a different color from the rest?

c) All faces have different colors?

Note: remember that, for example, the two paintings below are considered the same because if we appropriately rotate one of them, we obtain the other!

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