
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 the function $f(x)=\frac{x}{x^{2}+1}$ defined on $\mathbb{R}$ and the function $g(x)=\frac{mx}{1+x}$ with domain $(-1,+\infty)$.
(1) If $g(x)=\frac{mx}{1+x}$ is decreasing on $(-1,+\infty)$, determine the range of values for the real number $m$ based on the definition of monotonicity;
(2) Under the condition of (1), if the function $h(x)=f(x)+g(x)$ has exactly two distinct zeros in the interval $(-1,1)$, determine the range of values for the real number $m$.

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