
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 equation about $x$, $(m+3)x^{|m|-2}+6m=0$ (Equation ①) has the same solution as $nx-5=x(3-n)$ (Equation ②), where Equation ① is a linear equation in one variable. 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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