
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
If $r_1$ and $r_2$ are the roots of the quadratic equation $x^2 + kx + \ell = 0$, find the values of $u$ such that the roots of a new quadratic equation $x^2 + ux + v = 0$ are $r_1^2$ and $r_2^2$.
A) $-k^2 + 2\ell$
B) $k^2 - 2\ell$
C) $-k^2 + \ell$
D) $k^2 + 2\ell$

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