
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 $f(x)=ax^{2}-b\ln x$, its tangent line at the point $(1,f(1))$ is $y=1$.

(1) Find the values of the real numbers $a$ and $b$.
(2) Determine whether there exists a real number $m$ such that when $x\in(0,1]$, the minimum value of the function $g(x)=f(x)-x^{2}+m(x-1)$ is $0$. If it exists, find the range of $m$; if not, explain the reason.

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