
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
Let the function $f(x)=x^{2}-m\ln x$, $h(x)=x^{2}-x+a$  
(I) When $a=0$, $f(x)\geqslant h(x)$ holds true over $(1,+\infty)$, find the range of the real number $m$;  
(II) When $m=2$, if the function $g(x)=f(x)-h(x)$ has exactly two distinct zeros on $[1,3]$, find the range of the real number $a$.

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