
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 $y = x - \frac{1}{x}$, transform the equation $x^6 + x^5 - 5x^4 + 2x^3 - 5x^2 + x + 1 = 0$ into a form involving $y$.
**A)** $x^2 (y^2 + y - 2) = 0$\
**B)** $x^2 (y^2 + y - 3) = 0$\
**C)** $x^2 (y^2 + y - 4) = 0$\
**D)** $x^2 (y^2 + y - 5) = 0$\
**E)** $\text{none of these}$

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