
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
If $a$, $b$, $c$, and $d$ are the roots of the equation $x^4 - bx - 5 = 0$, find an equation whose solutions are $\left(\dfrac{a + b + c}{d}\right)^2, \left(\dfrac{a + b + d}{c}\right)^2, \left(\dfrac{a + c + d}{b}\right)^2, \left(\dfrac{b + c + d}{a}\right)^2$.

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