
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
Let  $m\ge 3$  and  $n$  be positive integers such that  $n>m(m-2)$ . Find the largest positive integer  $d$  such that  $d\mid n!$  and  $k\nmid d$  for all  $k\in\{m,m+1,\ldots,n\}$ .

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