
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. For instance, July 19 is relatively prime since 7 and 19 have no common divisors other than 1. Identify the month with the fewest relatively prime dates when February has 29 days (leap year). How many relatively prime dates are in that month?

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