
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
During a medical outreach activity, a hospital arranges for 2 male and 2 female doctors to work in three rural hospitals. Each hospital must be assigned at least one doctor, and the male doctors must not be assigned to the same rural hospital. Calculate the total number of different arrangement methods.

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