
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 $n$ $(n > 1)$ such that if $a_{1} < a_{2} < \cdots < a_{k}$ are the positive integers less than $n$ that are relatively prime to $n$, then $a_{i} + a_{i+1}$ $(i = 1, 2, \cdots, k-1)$ is not divisible by 3.

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