
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 city, public rental housing is available in four districts: A, B, C, and D. It is assumed that each applicant applies for housing in only one district, and the choice of district is equally likely for all applicants. For three applicants in the city, labeled as 甲, 乙, and 丙:  
（1）Calculate the total number of possible application scenarios;  
（2）Calculate the probability that applicants 甲 and 乙 apply for housing in the same district.

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