
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
Consider a year where each month has a unique number of days ranging from 28 to 31. A relatively prime date is a date for which the number of the month and the number of the day are relatively prime. For example, March 4 is not a relatively prime date because the greatest common factor of 3 and 4 is greater than 1. Given that September has 30 days and is represented by the number 9, calculate how many relatively prime dates are in September.

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