
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, one side is purple, and four sides are orange. How many different such cubes can be painted? Two cubes are considered the same if one cube can be rotated in any way to match the second cube.

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