
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 three real roots of the equation \( \sqrt{2025} x^3 - 4050x^2 - 4 = 0 \). Find \( x_2(x_1+x_3) \).

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