
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
Find all positive integers  $k > 1$  for which there exists a positive integer  $n$  such that  $\tbinom{n}{k}$  is divisible by  $n$ , and  $\tbinom{n}{m}$  is not divisible by  $n$  for  $2\leq m < k$ .

*Merlijn Staps*

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