
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 that $r_1$ and $r_2$ are the roots of the quadratic equation $x^2 - ax + b = 0$, find the equation whose roots are $r_1^2 + r_2$ and $r_1 + r_2^2$.
A) $x^2 - (a^2 + a - 3b)x + (a^3 - 3ab + b)$
B) $x^2 - (a^2 - a - 2b)x + (a^3 - ab)$
C) $x^2 - (a^2 + a - 2b)x + (a^3 - ab)$
D) $x^2 - (a^2 + 2a - 2b)x + (a^4 - ab)$

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