
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
Let the function $f(x) = \frac{mx}{1+|x|}$ (where $|m| > 1$), and the interval $M=[a, b]$ ($a < b$), with the set $N=\{y|y=f(x), x \in M\}$. Then, the number of real pairs $(a, b)$ that make $M=N$ true is $\boxed{\text{1 or 3}}$.

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