
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 power function $f(x)=({3{m^2}-2m}){x^{m-\frac{1}{2}}}$ is monotonically increasing on $\left(0,+\infty \right)$, and $g\left(x\right)=-3^{x}+t$.  
$(1)$ Find the value of the real number $m$;  
$(2)$ When $x\in \left[1,4\right]$, let the ranges of $f\left(x\right)$ and $g\left(x\right)$ be sets $A$ and $B$ respectively. Given proposition $p:x\in A$ and proposition $q:x\in B$, if proposition $q$ is a necessary but not sufficient condition for proposition $p$, find the range of the real number $t$.

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