
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 $f(x)=x-a\ln x$ ($a\in \mathbb{R}$).
- (1) Discuss the number of extreme points of the function $f(x)$ within its domain.
- (2) Let $g(x)=- \frac {a+1}{x}$. If the inequality $f(x) > g(x)$ holds for any $x\in[1,e]$, find the range of $a$.

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