
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 that the solutions of the equations $(m+3)x^{|m|-2}+6m=0\ldots①$ and $nx-5=x(3-n)\ldots②$ with respect to $x$ are the same, where equation $①$ is a first-degree equation, find the value of the algebraic expression $(m+x)^{2000}\cdot(-m^2n+xn^2)+1$.

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