
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
Let  $n>1$  be a positive integer and  $d_1<d_2<\dots<d_m$  be its  $m$  positive divisors, including  $1$  and  $n$ . Lalo writes the following  $2m$  numbers on a board:
\[d_1,d_2\dots, d_m,d_1+d_2,d_2+d_3,\dots,d_{m-1}+d_m,N \]
where  $N$  is a positive integer. Afterwards, Lalo erases any number that is repeated (for example, if a number appears twice, he erases one of them). Finally, Lalo realizes that the numbers left on the board are exactly all the divisors of  $N$ . Find all possible values that  $n$  can take.

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