
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
Five students, A, B, C, D, and E, went to help the elderly in four nursing homes, with each student visiting only one nursing home and each nursing home having at least one student. Determine the probability that both A and B visit the same nursing home.

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