
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 equation whose roots are $cr+b$ and $cs+b$ where $r$ and $s$ are the roots of the quadratic equation $ax^2 + bx + c = 0$.
A) $ax^2 + (bc - 2ab)x + c^3 - b^2c + ab^2 = 0$
B) $ax^2 - (bc - 2ab)x + c^3 - b^2c + ab^2 = 0$
C) $ax^2 - (bc + 2ab)x + c^2 - b^2c + ab^2 = 0$
D) $ax^2 + (bc + 2ab)x + c^3 - b^2c = 0$

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