
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
Positive numbers \(a\), \(b\), and \(c\) satisfy the following equations:

\[ a^{2} + a b + b^{2} = 1 \]
\[ b^{2} + b c + c^{2} = 3 \]
\[ c^{2} + c a + a^{2} = 4 \]

Find \(a + b + c\).

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