
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 $f(x) = e^{mx} + x^{4} - mx$.  
$(1)$ Find the monotonic intervals of $f(x)$.  
$(2)$ If for any $x_{1}$, $x_{2} \in [-2,2]$, $|f(x_{1}) - f(x_{2})| \leq e^{4} + 11$, find the range of $m$.

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