
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
A relatively prime date is a date for which the number of the month and the number of the day are relatively prime. Identify the month with the fewest relatively prime dates among the months with 31 days, and calculate how many such dates are present.

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