
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 $f\left(x\right)=-x^{2}+mx-m$.  
$(1)$ If the maximum value of the function $f\left(x\right)$ is $0$, find the value of the real number $m$.  
$(2)$ If the function $f\left(x\right)$ is monotonically decreasing on $\left[-1,0\right]$, find the range of the real number $m$.  
$(3)$ Does there exist a real number $m$ such that the range of the function $f\left(x\right)$ on $\left[2,3\right]$ is exactly $\left[2,3\right]$? If yes, find the value of the real number $m$; if not, explain the reason.

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