
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
Divide the 12 positive integers from 1 to 12 into two groups, Group A and Group B, such that the average of the numbers in Group A is 2 greater than the average of the numbers in Group B. How many numbers are there in Group A?

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