
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
Consider the polynomial expression $x[x\{x(3-x)-6\}+12] + 2$. For all real numbers \(x\), simplify the expression completely.
A) \( -x^4 + 4x^3 - 6x^2 + 12x + 2 \)
B) \( -x^4 + 3x^3 - 5x^2 + 12x + 2 \)
C) \( -x^4 + 3x^3 - 6x^2 + 12x + 2 \)
D) \( x^4 - 3x^3 + 6x^2 - 12x - 2 \)
E) \( -x^4 + 3x^3 - 6x^2 + 11x + 2 \)

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