
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 $f(x)= \frac {1}{2}x^{2}-ax+\ln x$, where $a\in\mathbb{R}$.  
(I) Discuss the number of extreme points of the function $f(x)$.  
(II) If the function $f(x)$ has two extreme points $m$ and $n$, where $m < n$ and $m > \frac { \sqrt {2}}{2}$, does there exist an integer $k$ such that the inequality $f(n)+k < f(m) < f(n)+3k+5\ln 2$ always holds? If it exists, find the value of the integer $k$; if not, explain why. (Reference data: $\ln 2\approx0.7$, $\ln 3\approx1.1$)

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