
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 $f(x) = e^x + mx - 1$ where $m \in \mathbb{R}$,
(I) Discuss the monotonicity of $f(x)$;
(II) If there exists a positive real number $x_0$ such that $f(x_0) = x_0\ln{x_0}$, find the maximum value of $m$;
(III) If $g(x)=\ln(e^x-1)-\ln{x}$ and the inequality $f(g(x)) < f(x)$ always holds for $x \in (0, +\infty)$, determine the range of the real number $m$.

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