
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 $$f(x)= \frac {1}{2}x^{2}-(3+m)x+3m\ln{x}$$, where $m\in\mathbb{R}$.  
(I) Find the intervals where the function $f(x)$ is monotonically increasing;  
(II) Let $A(x_1, f(x_1))$ and $B(x_2, f(x_2))$ be any two distinct points on the graph of the function $f(x)$. If the slope of the line $l$ passing through points A and B is always greater than -3, find the range of values for $m$.

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