
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 $-8{x^3}{y^{m+1}}+x{y^2}-\frac{3}{4}{x^3}+6y$ is a sixth-degree quadrinomial, and the monomial $\frac{2}{5}π{x^n}{y^{5-m}}$ has the same degree as this polynomial.<br/>$(1)$ Find the values of $m$ and $n$;<br/>$(2)$ Find the sum of the coefficients of the polynomial.

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