
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
A cube is painted so that one side is yellow, two sides are purple, and three sides are orange. How many different such cubes can be painted, considering two cubes identical if one can be rotated to match the other?

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