
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
Given the quadratic equation \(x^{2} + px + q = 0\). Find the equation whose roots: 1) would differ from the roots of the given equation only by their signs, 2) would be the reciprocals of the roots of the given equation.

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