
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 natural numbers from 1 to 2010 into groups, such that the greatest common divisor of any three numbers within each group is 1. What is the minimum number of groups required?

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