
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
Find the value of $p$ in terms of $a$ and $b$ if $r_1$ and $r_2$ are the roots of $x^2 + ax + b = 0$, and $r_1^2$ and $r_2^2$ are the roots of $x^2 + px + q = 0$.
A) $-a^2 + 2b$
B) $a^2 - 2b$
C) $-a^2 - 2b$
D) $a^2 + 2b$

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