
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  $n \ge 2$  can one find a sequence of distinct positive integers  $a_1, a_2, \ldots , a_n$  so that the sum  $$ \frac{a_1}{a_2} + \frac{a_2}{a_3} + \ldots +\frac{a_n}{a_1} $$   is an integer?

*(3 points)*

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