
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
We say that  $A$  $=$ { $a_1,a_2,a_3\cdots a_n$ } consisting  $n>2$  distinct positive integers is  $good$  if for every  $i=1,2,3\cdots n$  the number  ${a_i}^{2015}$  is divisible by the product of all numbers in  $A$  except  $a_i$ . Find all integers  $n>2$  such that exists a  $good$  set consisting of  $n$  positive integers.

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