
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
How many unordered pairs of coprime numbers are there among the integers 2, 3, ..., 30? Recall that two integers are called coprime if they do not have any common natural divisors other than one.

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