
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 $f(x)= \frac {1}{2}x^{2}+mx+m\ln x$  
(I) Discuss the monotonicity of the function $f(x)$;  
(II) When $m=1$, if the equation $f(x)= \frac {1}{2}x^{2}+ac$ has a unique real solution in the interval $[\frac {1}{e},+\infty)$, find the range of the real number $a$;  
(III) When $m > 0$, if for any two real numbers $x_{1}$, $x_{2}$ in the interval $[1,2]$ with $x_{1} < x_{2}$, the inequality $|f(x_{1})-f(x_{2})| < x_{2}^{2}-x_{1}^{2}$ holds, find the maximum value of the real number $m$.

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