
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 passes through the points $\left(1,0\right)$ and $\left(0,2\right)$.  
$(1)$ Find the analytical expression of this linear function.  
$(2)$ If the point $P\left(m,n\right)$ lies on the graph of this linear function, when $-2 \lt m\leqslant 3$, find the range of values for $n$.

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