
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 $f(x)= \dfrac {1+a}{x}$ ($a\in\mathbb{R}$).  
(I) When $a=0$, find the equation of the tangent line to the curve $f(x)$ at $x=1$;  
(II) Let the function $h(x)=a\ln x-x-f(x)$, find the extreme values of the function $h(x)$;  
(III) If $g(x)=a\ln x-x$ has a point $x_{0}$ in the interval $[1,e]$ ($e=2.71828…$) such that $g(x_{0})\geqslant f(x_{0})$ holds, find the range of values for $a$.

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