
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
For all positive integers  $n$ , let  $f(n)$  return the smallest positive integer  $k$  for which  $\tfrac{n}{k}$  is not an integer.  For example,  $f(6) = 4$  because  $1$ ,  $2$ , and  $3$  all divide  $6$  but  $4$  does not.  Determine the largest possible value of  $f(n)$  as  $n$  ranges over the set  $\{1,2,\ldots, 3000\}$ .

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