
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 $f(x)=\ln x+a(1-\frac{1}{x})$, where $a\in R$.

(1) If $a=-1$, find the minimum value of $f(x)$;

(2) If $f(x)\geqslant 0$ holds for all $x\geqslant 1$, find the range of $a$.

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