
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 $f(x)= \frac {1}{3}x^{3}- \frac {1}{2}(a+2)x^{2}+2ax$, $g(x)= \frac {1}{2}(a-5)x^{2}(a\geqslant 4)$.  
(I) Find the monotonic intervals of $f(x)$;  
(II) If the slope of the tangent line at any point $P(x_{0},y_{0})$ on the graph of $f(x)$ is $k\geqslant - \frac {25}{4}$, find the range of $a$;  
(III) If for any two distinct real numbers $x_{1}$, $x_{2}$ in the interval $[3,4]$, $|f(x_{1})-f(x_{2})| > |g(x_{1})-g(x_{2})|$ holds, find the range of $a$.

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