
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
Suppose that  $\{a_n\}$  is a sequence such that  $a_{n+1}=(1+\frac{k}{n})a_{n}+1$  with  $a_{1}=1$ .Find all positive integers  $k$  such that  any  $a_n$  be integer.

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