
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
Given the real numbers \(x_{1}, x_{2}, x_{3}\) such that: 
\[ x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{1} x_{2} + x_{2} x_{3} = 2 \]
find the maximum value of \(\left|x_{2}\right|\).

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