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

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