
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 universe set be $U = \{(x, y) | x \in \mathbb{R}, y \in \mathbb{R}\}$. Define two sets $A = \{(x, y) | 2x - y + m > 0\}$ and $B = \{(x, y) | x + y - n \leq 0\}$. Find the necessary and sufficient condition for the point $P(2, 3)$ to belong to the intersection $A \cap (\complement_U B)$.

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