
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
Let the function be $$f(x)= \frac {x^{3}}{3}-(a+1)x^{2}+4ax+b，\text{where} \, a, b \in \mathbb{R}$$  
(I) If the function $f(x)$ has a minimum value of $$\frac {1}{2}$$ at $x=3$, find the values of $a$ and $b$;  
(II) Find the intervals of monotonic increase for the function $f(x)$;  
(III) If the function $f(x)$ has exactly one extremum in the interval $(-1, 1)$, find the range of the real number $a$.

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