
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 $f(x)=\ln (1+x)-mx$, where $m\in \mathbb{R}$.

$(1)$ If $m=1$, find the interval where the function $f(x)$ is monotonically decreasing;

$(2)$ Find the extreme values of the function $f(x)$;

$(3)$ If the function $f(x)$ has exactly two zeros in the interval $\left[ 0,e^{2}-1 \right]$, find the range of $m$.

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