
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. Consider a month with 31 days and the number of the month having multiple small prime divisors. Determine how many relatively prime dates are in December, given that December has 31 days and the number 12 as its month number which factors into $2^2 \cdot 3$.

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