
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 $f(x)=x-a\ln x+ \frac {1+a}{x}$ $(a\in\mathbb{R})$  
$(1)$ Find the intervals of monotonicity for $f(x)$;  
$(2)$ If a point $x_{0}$ is chosen from the interval $[1,e]$ $(e=2.71828…)$ such that $f(x_{0})\leqslant 0$ holds, find the range of values for $a$.

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