
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
Suppose $p$, $q$, $r$, and $s$ are the roots of the equation $x^4 + 4x^3 - 5 = 0$. Find an equation whose solutions are:
\[
\frac{p+q+r}{s^3}, \frac{p+q+s}{r^3}, \frac{p+r+s}{q^3}, \frac{q+r+s}{p^3}
\]
A) $5x^6 + 4x + 5 = 0$
B) $5x^6 + x^3 - 4 = 0$
C) $5x^6 - x^2 + 4x = 0$
D) $x^6 + 4x^3 - 5 = 0$
E) $x^6 - 5x^3 + 4 = 0$

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