
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
How many positive integers \(n\) are there such that \(n\) is a multiple of \(5\) under \(120\), and the least common multiple of \(5!\) and \(n\) equals \(6\) times the greatest common divisor of \(4!\) and \(n?\)
A) 3  
B) 5  
C) 7  
D) 9  
E) 11

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