
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
We color each face of a cube either red, white, or green. The color of each face is chosen randomly and independently. Each color is equally likely to be chosen. What is the probability that there will be at least one pair of opposite faces with the same color?

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