
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 sets of integers  $n\geq 2$  and positive integers  $(a_1, a_2, \dots, a_n)$  that satisfy all of the following conditions:


- $a_1 < a_2 < \cdots < a_n$
- $a_n$  is a prime number.
- For any integer  $k$  between  $1$  and  $n$ ,  $a_k$  divides  $a_1+a_2+\cdots+a_n$ .


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