
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
Given the inequality about $x$, $2x - 1 > m(x^2 - 1)$.
(1) Does there exist a real number $m$ such that the inequality holds for any $x \in \mathbb{R}$? Explain your reasoning.
(2) If the inequality holds for $m \in [-2, 2]$, find the range of real numbers $x$.

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