
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 face is blue, two faces are red, and the remaining three faces are green. How many distinct ways can such a cube be painted, taking into account that two red faces can also be placed opposite each other? Assume two cubes are considered the same if one can be rotated to match the other.

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