
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
Let \( a, b, c \) be not necessarily distinct natural numbers such that the fractions \( \frac{a+b}{c}, \frac{a+c}{b}, \frac{b+c}{a} \) are also natural numbers. Find all possible values of the sum \( \frac{a+b}{c} + \frac{a+c}{b} + \frac{b+c}{a} \).

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