
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
In a bag, there are several balls of the same size and shape. Among them, there is 1 ball labeled '0', 1 ball labeled '1', and $n$ balls labeled '2'. It is known that when randomly drawing 1 ball from the bag, the probability of drawing a ball labeled '2' is $\frac{1}{3}$.  
(1) Find the value of $n$;  
(2) Draw 2 balls from the bag without replacement. Let the label of the first ball drawn be $a$, and the label of the second ball drawn be $b$. Let event A be "a + b = 2". Find the probability of event A.

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