
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 $f(x)=x-\frac{2a-1}{x}-2a\ln x$, $(a\in R)$
(I) When $a=\frac{3}{2}$, find the monotonic intervals of the function $f(x)$;
(II) If $f(x)\geqslant 0$ holds for any $x\in[1,+\infty]$, find the range of values for the real number $a$.

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