
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
You have two blackboards  $A$  and  $B$ . You have to write on them some of the integers greater than or equal to  $2$  and less than or equal to  $20$  in such a way that each number on blackboard  $A$  is co-prime with each number on blackboard  $B.$  Determine the maximum possible value of multiplying the number of numbers written in  $A$  by the number of numbers written in  $B$ . 

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