
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 $f(x)=x- \frac {1}{x}-m\ln x$  
$(1)$ If the function $f(x)$ is increasing on its domain, find the range of $m$;  
$(2)$ Under the condition of $(1)$, if the function $h(x)=x-\ln x- \frac {1}{e}$, and there exist $x_{1}$, $x_{2} \in [1,e]$ such that $f(x_{1}) \geqslant h(x_{2})$ holds, find the range of $m$.

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