
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 functions $f(x)= \frac {\ln x}{x}$ and $g(x)=x(\ln x- \frac {ax}{2}-1)$.   
(I) Find the maximum value of $y=f(x)$.  
(II) When $a\in[0, \frac {1}{e}]$, find the range of the minimum value $h(a)$ of the function $y=g(x)$, where $x\in(0,e]$.

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