
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 $f(x)=x-a\ln x$, $g(x)=- \frac {1+a}{x}(a > 0)$  
$(1)$ If $a=1$, find the extreme values of $f(x)$;  
$(2)$ If there exists $x_{0}\in[1,e]$ such that $f(x_{0}) < g(x_{0})$ holds, find the range of the real number $a$.

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