
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
In the Cartesian coordinate system, the graph of a linear function $y=kx+b$ (where $k$ and $b$ are constants, and $k\neq 0$) passes through the points $\left(1,0\right)$ and $\left(0,2\right)$.
$(1)$ When $-2 \lt x\leqslant 3$, find the range of $y$;
$(2)$ Given that the point $P\left(m,n\right)$ lies on the graph of this function, and $m-n=4$, find the coordinates of point $P$.

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