
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 $f(x)=x+ \frac {\alpha}{x}+\ln x$ $(\alpha\in\mathbb{R})$  
$(1)$ Find the monotonic intervals and the extremum points of the function $f(x)$;  
$(2)$ If for $\forall\alpha\in\left[ \frac {1}{e},2e^{2}\right]$, the function $f(x)$ satisfies $f(x) < m$ for $\forall x\in[l,e]$, find the range of the real number $m$ (where $e$ is the base of the natural logarithm).

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