
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
If \( n \) is a positive integer and \( 2n \) has 28 positive factors and \( 3n \) has 30 positive factors, calculate the number of positive factors of \( 6n \).

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