
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
Of the numbers 1, 2, 3, ..., 20, which number has the greatest number of divisors, and what is the least common multiple (LCM) of the numbers with the most divisors?

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