
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
New definition: In the Cartesian coordinate system, for point $P(m,n)$ and point $P'(m,n')$, if $m\geqslant 0$, then $n' = n-4$; if $m \lt 0$, then $n' = -n$. Point $P'(m,n')$ is called the limited variable point of point $P(m,n)$. For example, the limited variable point of point $P_{1}(2,5)$ is $P_{1}'(2,1)$, then the limited variable point of point $P_{2}(-2,3)$ is ____. If point $P(m,n)$ lies on the graph of the quadratic function $y=-x^{2}+4x+2$, then the range of the ordinate $n'$ of its limited variable point $P'$ when $-1\leqslant m\leqslant 3$ is ____.

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