
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 $y=(k+2){x}^{k^{2}+k-4}$ is a quadratic function, and when $x \lt 0$, $y$ increases as $x$ increases.  
$(1)$ Find the value of $k$;  
$(2)$ If point $P(m,n)$ lies on the graph of this quadratic function, and $-2\leqslant m\leqslant 1$, then the range of values for $n$ is ______.

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