
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 $f(x)=a\ln x$, where $a\in\mathbb{R}$.  
(I) If the curve $y=f(x)$ and the curve $g(x)= \sqrt {x}$ have a common tangent line at their intersection point, find the value of the real number $a$;  
(II) Under the condition of (I), does the function $F(x)=xf(x)- \frac {xe^{1-x}}{2}+1$ have a zero? If so, find the zero; if not, please explain why.

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