
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
Vasya and Petya each chose two different numbers, and each of their numbers has as many prime factors as composite factors. Can Vasya and Petya's numbers have common divisors greater than 1?

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