
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
It is known that \(a^{2} b + a^{2} c + b^{2} a + b^{2} c + c^{2} a + c^{2} b + 3 a b c = 30\) and \(a^{2} + b^{2} + c^{2} = 13\).

Find \(a + b + c\).

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