
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 functions $f(x)= \frac {1}{2}x^{2}-2x$ and $g(x)=a\ln x$.  
$(1)$ Discuss the monotonic intervals of the function $y=f(x)-g(x)$.  
$(2)$ Let $h(x)=f(x)-g(x)$. If for any two unequal positive numbers $x_{1}$, $x_{2}$, it always holds that $\frac {h(x_{1})-h(x_{2})}{x_{1}-x_{2}} > 2$, find the range of the real number $a$.

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