
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 $y = x + \frac{1}{x}$, simplify the equation $x^4 + x^3 - 7x^2 + x + 1 = 0$ using the expression for $y$.
A) $x^2(y^2 + y - 7) = 0$
B) $x^2(y^2 + y - 8) = 0$
C) $x^2(y^2 + y - 9) = 0$
D) $x^2(y^2 + y - 10) = 0$
E) None of these

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