
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
In a certain city, public rental housing is located in three communities: $A$, $B$, and $C$. Each applicant can only apply for a house in one of these communities, and the probability of applying for a house in any of the communities is equal. What is the probability that exactly 2 out of 4 applicants choose to apply for a house in community $A$?

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