
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
There are two cafeterias, $A$ and $B$, in a school. If three students, $a$, $b$, and $c$, each randomly choose one of the cafeterias for their meal, what is the probability that none of them will dine in the same cafeteria?

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