
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 \(x^{3}+p x^{2}+q x+r=0\).

1) Form an equation with roots \(x_{1} x_{2}, x_{2} x_{3}, x_{1} x_{3}\);
2) Use the result from part 1 to find the roots of the equation \(x^{3}-3 \sqrt{2} x^{2}+7 x-3 \sqrt{2}=0\).

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