
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
The roots of the cubic equation $Ax^3 + Bx^2 + Cx + D = 0$ are $u$, $v$, and $w$. If the quadratic equation $x^2 + px + q = 0$ has roots $u^2$, $v^2$, then find the value of $p$ in terms of $A$, $B$, $C$, and $D$.
A) $\frac{B^2 - 2C}{A^2}$
B) $\frac{2C - B^2}{A^2}$
C) $\frac{B^2}{A^2}$
D) $\frac{2B^2 - C}{A^2}$
E) $\frac{C - B^2}{A^2}$

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