
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
Let the universal set $U=\{(x,y)\,|\,x, y \in \mathbb{R}\}$, and consider the sets $$M=\left\{(x,y) \middle| \frac{y+2}{x-2}=1\right\}$$ and $$N=\left\{(x,y) \middle| y \neq x-4\right\}.$$ Determine the set $$(\complement_U M) \cap (\complement_U N).$$

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