
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 $f(x)=a\ln x- \frac {1}{x}$, where $a\in\mathbb{R}$.  
$(I)$ If the tangent line of the curve $y=f(x)$ at the point $(1,f(1))$ is perpendicular to the line $x+2y=0$, find the value of $a$;  
$(II)$ When $a=1$, determine whether the curve $y=f(x)$ and the line $y=2x-3$ have any common points. If they do, find all the common points; if not, explain why.

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