
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
Find all positive integers  $n$  that have distinct positive divisors  $d_1, d_2, \dots, d_k$ , where  $k>1$ , that are in arithmetic progression and   $$ n=d_1+d_2+\cdots+d_k. $$   Note that  $d_1, d_2, \dots, d_k$  do not have to be all the divisors of  $n$ .

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