
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
Anya has blue, green, and red paints. She wants to paint a wooden cube in such a way that each of the cube's faces is painted with one of these colors and there are exactly two faces of each color. In how many distinct ways can she do this? Note that painting arrangements that can be obtained by rotating the cube are considered identical.

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