
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 $y = x + \frac{1}{x}$, then what does the equation $x^3+x^2-6x+1 = 0$ transform to using $y$?
A) $y^2 + y - 8 = 0$
B) $x^2(y^2 + y - 7) = 0$
C) $x(x^2y - 6) + 1 = 0$
D) $x^2(y^2 + y - 5) = 0$
E) None of these

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