
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
A positive integer  $n$  is called  $\textit{un-two}$  if there does not exist an ordered triple of integers  $(a,b,c)$  such that exactly two of  $$ \dfrac{7a+b}{n},\;\dfrac{7b+c}{n},\;\dfrac{7c+a}{n} $$  are integers. Find the sum of all un-two positive integers.

*Proposed by **stayhomedomath***

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