
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 $f(x)=x-a\ln x$ and $g(x)=- \frac {1+a}{x}$ ($a∈R$).
(I) Find the monotonic intervals of the function $h(x)=f(x)-g(x)$;
(II) If the inequality $f(x)\leqslant g(x)$ has a non-empty solution set in the interval $[1,e]$ ($e=2.71828…$), find the range of the real number $a$.

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