
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
There are two blackboards \( A \) and \( B \), each with several different integers written on them, where each integer is not less than 2 and not greater than 20. If each time you pick one number from blackboard \( A \) and one from blackboard \( B \), these two numbers are always coprime. Find the maximum possible value of the product of the number of integers written on blackboard \( A \) and the number of integers written on blackboard \( B \).

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