
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
Without solving the quadratic equation \( x^{2} + px + q = 0 \), formulate a new equation where one of the roots is the sum of the cubes of the roots of the given equation, and the other is the cube of their sum.

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