
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 month with 31 days and a number forming by multiplying the two smallest primes, i.e., prime factorization is $2 * 3$. Evaluate the number of days which are relatively prime to the month's number.

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