
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 set A = {1,2}, and B = {1,2,3}. Randomly select a number $a$ from set A and a number $b$ from set B to determine a point $P(a, b)$ on the plane. Define event $C_n$ as "Point $P(a, b)$ lies on the line $x + y = n$" (where $2 \leq n \leq 5$, $n \in \mathbb{N}$). If the probability of event $C_n$ is maximal, then the possible values of $n$ are _______.

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