
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 $f(x)=x\ln x- \frac {a}{2}x^{2}$, and the line $l$: $y=(k-2)x-k+1$, where $k\in\mathbb{Z}$.  
$(1)$ If there exists $x_{0}\in[e,e^{2}]$ such that $f(x_{0}) > 0$ holds, find the range of values for the real number $a$;  
$(2)$ Let $a=0$, when $x > 1$, the graph of the function $f(x)$ is always above the line $l$, find the maximum value of $k$.

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