
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
A student was studying the function $f(x)=\frac{x}{1+|x|} (x\in\mathbb{R})$ and proposed the following conclusions:
1) $f(-x)+f(x)=0$ always holds true for $x\in\mathbb{R}$;
2) The range of the function $f(x)$ is $(-1,1)$;
3) If $x_1\neq x_2$, then $f(x_1)\neq f(x_2)$;
4) The function $g(x)=f(x)-x$ has three roots on $\mathbb{R}$.
Identify the correct conclusion(s).

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