
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 the roots $r_1$ and $r_2$ of the quadratic equation $x^2 - nx + p = 0$, find the constants $u$ and $v$ for which $r_1^4$ and $r_2^4$ are the roots of the new quadratic equation $x^2 + ux + v = 0$.
A) $u = n^4 - 4pn^2 + 2p^2$, $v = p^4$
B) $u = -(n^4 - 4pn^2 + 2p^2)$, $v = p^3$
C) $u = -(n^4 - 4pn^2 + 6p^2)$, $v = p^4$
D) $u = -(n^4 - 4pn^2 + 2p^2)$, $v = p^4$

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