
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
Consider two polynomial equations:
1. $x^2 - ax + b = 0$, the roots of which are $\alpha$ and $\beta$.
2. A new equation $x^2 - px + q = 0$, where the roots are $\alpha^2 + \beta^2$ and $\alpha\beta$.

Find the expression for $p$ in terms of $a$ and $b$.
A) $a^2$
B) $a^2 - 2b$
C) $a^2 - b$
D) $2a^2 - b$

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