
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 $A=5x^{2}-mx+1$, $B=2x^{2}-2x-n$ ($A$, $B$ are polynomials in terms of $x$), and the result of $A-B$ does not contain linear terms or constant terms.  
$(1)$ Find the values of $m$ and $n$;  
$(2)$ Find the value of $m^{2}+n^{2}-2mn$.

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