
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 $$f(x)=a\ln x+ \frac {1}{x} \quad (a\in\mathbb{R})$$  
(1) When $a=2$, find the extreme values of the function $y=f(x)$;  
(2) If the function $g(x)=f(x)-2x$ is monotonically decreasing on $(0, +\infty)$, find the range of $a$;  
(3) When $a>0$, discuss the number of zeros of the function $y=f(x)$.

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