
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
In the era of "Internet$+$", there is a method of producing passwords using the "factorization method": factorizing a polynomial. For example, factorizing the polynomial $x^{3}-x$ results in $x\left(x+1\right)\left(x-1\right)$. When $x=20$, $x-1=19$, $x+1=21$, we can obtain the numerical password $201921$, or $192021$. After factorizing the polynomial $x^{3}+\left(m-n\right)x^{2}+nx$, and using the method shown in the question, when $x=10$, we can obtain the password $101213$. Find $m=$______ and $n=\_\_\_\_\_\_$.

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