
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
Determine the nature of the roots for the polynomial equation $x^4 - 6x^3 + 11x^2 - 6x + 1 = 0$.
A) All roots are positive.
B) 2 positive and 3 negative roots.
C) 4 positive and 1 negative roots.
D) 1 or 3 negative roots, with irrational positive roots.
E) 3 or 1 negative rooting, with irrational positive roots.

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