
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 $f\left(x\right)=(m^{2}-2m-2)x^{m}$, and $f\left(x\right)$ is monotonically increasing on $\left(0,+\infty \right)$.  
$(1)$ Find the value of $m$;  
$(2)$ Let $g\left(x\right)=f\left(x\right)+2x-3$, find the range of $g\left(x\right)$ on $\left[-1,3\right]$.

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