
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 the polynomial $\left(m-3\right)x^{|m|-2}y^{3}+x^{2}y-2xy^{2}$ is a fourth-degree trinomial in terms of $x$ and $y$.  
$(1)$ Find the value of $m$;  
$(2)$ When $x=\frac{3}{2}$ and $y=-1$, find the value of this polynomial.

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