
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
Find all $x$ for which the inequality $\frac{x^2 - 4.5}{x^2-1} \leq 0$ holds.
A) $(-\infty, -1) \cup (1, \infty)$  
B) $(-\frac{3\sqrt{2}}{2}, \frac{3\sqrt{2}}{2})$  
C) $(-\frac{3\sqrt{2}}{2}, -1) \cup (-1, 1) \cup (1, \frac{3\sqrt{2}}{2})$  
D) $x \in \mathbb{R}$ except $x = \pm1$  
E) $(\frac{3\sqrt{2}}{2}, \infty) \cup (-\infty, -\frac{3\sqrt{2}}{2})$

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