
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 that $a$, $b$, $c$, and $d$ are the roots of the polynomial equation $x^4 + 5x - 4 = 0$, find an equation that has the roots 
\[\frac {a+b+c}{d^2}, \frac {a+b+d}{c^2}, \frac {a+c+d}{b^2}, \frac {b+c+d}{a^2}\]
A) $4x^4 + 5x^3 - 1 = 0$
B) $4x^4 - 5x^3 - 1 = 0$
C) $4x^4 + 5x^3 + 1 = 0$
D) $4x^4 - 5x^3 + 1 = 0$

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