
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 such that one side is blue, two sides are yellow, and three sides are red. How many different such cubes can be painted assuming that two cubes are the same if one can be rotated to become the other?

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