
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
When studying the function $f(x)=\frac{x}{|x|+1}$ for $x\in \mathbb{R}$, the following conclusions are drawn:<br/>① The function $f(x)$ is an odd function;<br/>② The range of the function $f(x)$ is $(-1,1)$;<br/>③ The function $f(x)$ is increasing on $\mathbb{R}$;<br/>④ Let $g(x)=f(x)-kx-k$, where $k\in \mathbb{R}$, then there exists a real number $k$ such that the function $g(x)$ has no zeros.<br/>Among them, the correct conclusions are: ______.

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