
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 roots of \(A x^{2}+B x+C=0\) be \(r\) and \(s\). Additionally, let the roots of \(x^{2}+p x+q=0\) be \(r^{2}\) and \(s^{2}\). Determine the value of \(p\) in terms of \(A\), \(B\), and \(C\).

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