
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 $f(x)=x^{2}-a\ln x$, where $a\in\mathbb{R}$.
(I) When $a=4$, find the minimum value of the function $f(x)$ on $[1,e]$ and the corresponding value of $x$;
(II) If there exists $x\in[2,e]$ such that $f(x)\geqslant (a-2)x$, find the range of the real number $a$.

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