
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 $f(x)=x-a\ln x$ ($a\in \mathbb{R}$).  
(I) When $a=2$, find the equation of the tangent line to the curve $f(x)$ at $x=1$;  
(II) Let the function $h(x)=f(x)+ \frac {1+a}{x}$, find the monotonic intervals of the function $h(x)$;  
(III) If $g(x)=- \frac {1+a}{x}$, there exists a point $x_{0}$ in $[1,e]$ ($e=2.71828\ldots$) such that $f(x_{0})\leqslant g(x_{0})$ holds, find the range of values for $a$.

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