
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 $x_1, x_2, x_3$ be the roots of the equation $\sqrt{2023}x^3 - 4047x^2 + 2 = 0$ with $x_1 < x_2 < x_3$. Find the value of $x_2(x_1 + x_3)$.

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