
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 $f(x)={x}^{-{m}^{2}+2m+3}$ $(m\in\mathbb{Z})$ is monotonically increasing in the interval $(0,+\infty)$ and is an even function.

$(1)$ Find the explicit formula of the function $f(x)$;

$(2)$ Let the function $g(x)=2 \sqrt{f(x)}-8x+q-1$. If $g(x) > 0$ holds for any $x\in[-1,1]$, find the range of the real number $q$.

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