
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 the equation \( x^{3} + p x + q = 0 \) have roots \( x_{1}, x_{2} \) and \( x_{3} \). Express the discriminant of this equation \( D = (x_{1} - x_{2})^{2} (x_{2} - x_{3})^{2} (x_{3} - x_{1})^{2} \) in terms of \( p \) and \( q \).

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