
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 proposition $p$: For any $x\in \left[0,1\right]$, the inequality $2x-2\geqslant m^{2}-3m$ always holds true; proposition $q$: There exists $x\in \left[-1,1\right]$, such that the inequality $x^{2}-x-1+m\leqslant 0$ holds true.<br/>$(1)$ If proposition $p$ is true, find the range of real number $m$; <br/>$(2)$ If propositions $p$ and $q$ have exactly one true proposition, find the range of real number $m$.

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