
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
$(1)$ Simplify first, then calculate the value: $7xy-2(5xy-2x^{2}y)+3xy$, where $x=1$, $y=-2$;<br/>$(2)$ If the polynomial $3x^{2}-nx^{m+1}y-x$ in terms of $x$ and $y$ is a cubic trinomial, and the coefficient of the highest degree term is $2$, find the value of $m^{2}+n^{3}$.

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