
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 parabola $y=\left(x-m\right)^{2}+n$ intersects the $x$-axis at points $\left(-1,0\right)$ and $\left(3,0\right)$, find the solutions to the equation $\left(x-1\right)^{2}+m^{2}=2m\left(x-1\right)-n$.

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