
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 sets $A={1,2}$ 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. Let the event $C_n$ be "Point $P(a,b)$ lies on the line $x+y=n (n \in \mathbb{N}^*)$". If the probability of event $C_n$ occurring is the greatest, then the value of $n$ is $\_\_\_\_\_\_$.

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