
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 $m\in R$, proposition $p:\forall x\in \left[0,2\right]$, $m\leqslant x^{2}-2x$, proposition $q:\exists x\in \left[0,+\infty \right)$, such that the equation $2^{x}+3=m$ holds.<br/>$(1)$ If $p$ is a true proposition, find the range of $m$;<br/>$(2)$ If $p\vee q$ is a true proposition, $p\wedge q$ is a false proposition, find the range of $m$.

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