
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 system of equations about $x$ and $y$: $\left\{\begin{array}{l}{3x+5y=m+2}\\{2x+3y=m}\end{array}\right.$, where the solution satisfies $x+y=-10$, find the value of the algebraic expression $m^{2}-2m+1$.

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