
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 $f(x)=\ln x+ \frac {1}{2}x^{2}- \frac {5}{2}x.$  
(I) Find the range of the function $f(x)$ on the interval $\left[ \frac {1}{4},2\right]$;  
(II) Let $x_{1}$, $x_{2}(x_{1} < x_{2})$ be the two extreme points of the function $g(x)=f(x)-(b- \frac {3}{2})x$, if $b\geqslant \frac {3}{2}$, and $g(x_{1})-g(x_{2})\geqslant k$ always holds, find the range of the real number $k$.

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