
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 the quadratic equations $x^2 + ax + b = 0$ and $x^2 + cx + d = 0$ where the roots of the first equation $\alpha$ and $\beta$ are transformed into the roots $\alpha^2 + 1$ and $\beta^2 + 1$ of the second equation. Determine the relation between $c$ and $a, b$.
A) \( c = -a^2 + 2b - 2 \)
B) \( c = -a^2 + 2b + 2 \)
C) \( c = a^2 - 2b + 2 \)
D) \( c = a^2 - 2b - 2 \)

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