
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 set of all $x$ for which the inequality $\frac{x^3 - x^2 - 6x}{x^2 - 3x + 2} > 0$ holds.
A) $x < -2$ or $-1 < x < 1$ or $x > 2$
B) $x < -1$ or $x > 3$
C) $-2 < x < 0$ or $1 < x < 2$ or $x > 3$
D) $x < -3$ or $-2 < x < 2$ or $x > 3$

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