
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
Let $a$, $b$, $c$, and $d$ be the solutions of the equation $x^4 - bx^2 - 6 = 0$. Find an equation whose solutions are:
\[
\frac{a + b}{c^3}, \frac{a + c}{b^3}, \frac{b + c}{a^3}, \frac{a + b + c}{d^3}
\]
A) $6y^2 + by - 1 = 0$
B) $6y^2 - by - 1 = 0$
C) $6y^2 + by + 1 = 0$
D) $y^2 - by - 6 = 0$
E) None of the above

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