
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 three sets, \( A = \{ x \mid x \in \mathbf{R} \text{ and } x > 1 \} \), \( B = \left\{ y \left\lvert y = \lg \frac{2}{x+1} , x \in A \right. \right\} \), \( C = \left\{ z \left\lvert z = \frac{m^{2} x - 1}{m x + 1}, x \in A \right. \right\} \). If \( C \subseteq B \), find the range of \( m \).

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