
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 $f(x)=e^{x}-a(x-1)$ $(a∈R)$.
$(1)$ Find the monotonic intervals of the function $f(x)$;
$(2)$ If $m$, $n$, $p$ satisfy $|m-p| < |n-p|$ always holds, then $m$ is closer to $p$ than $n$. Under the condition that the function $f(x)$ has an extreme value, when $x≥1$, $\frac {e}{x}$ is closer to $\ln x$ than $e^{x-1}+a$, try to find the range of $a$.

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