
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
$(1)$ Xiao Ming, after combining like terms in the polynomial $2x^{2}+ax-y+6-bx^{2}+3x-5y+1$, found that there were no terms containing $x$ or $x^{2}$. Find the value of $\left(a-b\right)^{2}$. <br/>$(2)$ Given the polynomial $-x^{2}+2y-mx+5-nx^{2}+6x-20y$ has a value independent of the variable $x$, determine the values of $m$ and $n$.

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