
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
Consider $kx^4 - 5kx - 12 = 0$ where $k$ is a nonzero constant, and $a, b, c, d$ are solutions of this equation. Then find a polynomial whose roots are $y_i = \frac{b+c+d}{ka^2}, \frac{a+c+d}{kb^2}, \frac{a+b+d}{kc^2}, \frac{a+b+c}{kd^2}$.
A) $12k^3 x^4 - 5k^3 x^3 - 1 = 0$
B) $12k^3 x^4 + 5k^3 x^3 + 1 = 0$
C) $5k^3 x^3 - 12k^3 x^4 + 1 = 0$
D) $x^4 - 5kx - 12 = 0$

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