
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 $f(x) = -\frac{x}{1+|x|}$ ($x \in \mathbb{R}$), and the set $N = \{y | y = f(x), x \in M\}$, where $M = [a, b]$ ($a < b$). Determine the number of real number pairs $(a, b)$ that satisfy $M = N$.

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