
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 $z = x - \frac{1}{x}$, then determine the new form of the polynomial $x^4 - 3x^3 - 2x^2 + 3x + 1 = 0$.
**A)** $x^2(z^2 - 3z + 2) = 0$  
**B)** $x^2(z^2 - 3z - 4) = 0$  
**C)** $x^2(z^2 - 3z) = 0$  
**D)** $x^2(z^2 - 3z + 1) = 0$  
**E)** None of these

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