
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
Three electric generators have powers \(x_{1}, x_{2}, x_{3}\), and the total power of all three does not exceed 2 MW. In a power system with such generators, a certain process is described by the function

\[ 
f\left(x_{1}, x_{2}, x_{3}\right)=\sqrt{x_{1}^{2}+x_{2} x_{3}}+\sqrt{x_{2}^{2}+x_{1} x_{3}}+\sqrt{x_{3}^{2}+x_{1} x_{2}}.
\]

Find the maximum and minimum values of this function.

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