
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
Given three students, A, B, and C, each randomly choose to join one of the clubs, "Traffic Volunteers" or "Traditional Culture Promotion", determine the probability that all three students do not join the same club.

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