
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
On a strip, the numbers from 1 to 1598 were written in order and then cut into several parts. It turned out that the arithmetic mean of all the numbers in the first part is equal to some natural number $n$, the arithmetic mean of the numbers in the second part is $2n$, the third part is $3n$, and so on. Explain for which $n$ this is possible.

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