
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 triples of positive integers $a \leq b \leq c$ that are primitive (i.e., they do not have any common prime factors) such that each one of them divides the sum of the other two.

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