
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
Dr. Lee has a class of 12 students. Every student can choose to be part of one of three clubs: Math, Science, or Art, with each choice being equally likely. What is the probability that the number of students in at least one club is not the same as in any other club?

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