
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 defined as a date where the month number and day number are relatively prime. Determine how many relatively prime dates are there in July, assuming July is chosen as potentially having one of the fewest relatively prime dates.

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