
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 that $-nx^{2}y^{m+1}+xy^{2}-3x^{5}-6$ is a seven-degree polynomial in terms of $x$ and $y$, and the coefficient of its highest degree term is $8$.  
$(1)$ Find the values of $m$ and $n$;  
$(2)$ Rearrange this polynomial in descending powers of $x$.

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