
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  $n, n>1$  for wich holds : 
If  $a_1, a_2 ,\dots ,a_k$  are all numbers less than  $n$  and relatively prime to  $n$  , and holds  $a_1<a_2<\dots <a_k $ , then none of sums  $a_i+a_{i+1}$  for  $i=1,2,3,\dots k-1 $  are divisible by  $3$ .

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