
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 $f(x)=ax+\frac{a-1}{x}-\ln x-1$, where $a > 0$.

(I) When $a=1$, find the monotonic intervals and extreme values of the function $f(x)$;

(II) If $f(x)\geqslant {0}$ holds for any $x\in [1,+\infty)$, find the range of positive values of $a$.

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