
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 which integers  $n \ge 2$  can we arrange numbers  $1,2, \ldots, n$  in a row, such that for all integers  $1 \le k \le n$  the sum of the first  $k$  numbers in the row is divisible by  $k$ ? 

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