
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 roots of the polynomial equation $x^4 - 7x^3 + 14x^2 - 7x - 2 = 0$. Find an equation whose solutions are $\dfrac{a + b + c + 4}{d}, \dfrac{a + b + d + 4}{c}, \dfrac{a + c + d + 4}{b}, \dfrac{b + c + d + 4}{a}$.

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