
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 inequality $\frac{x^3 - 4x}{x^2 - 4x + 3} > 0$. Determine the set of $x$-values that satisfy this inequality.
A) $x \in (-\infty, -2) \cup (-2, 0) \cup (1, 2) \cup (3, \infty)$  
B) $x \in (-2, 0) \cup (3, \infty)$  
C) $x \in (0, 2) \cup (2, 3)$  
D) $x \in (-2, 2)$

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