
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
There are two bags, bag A and bag B. Bag A contains three balls labeled as 1, two balls labeled as 2, and one ball labeled as 3. Bag B contains two balls labeled as 1, one ball labeled as 2, and one ball labeled as 3. If we first randomly select one ball from bag A and put it into bag B, and then select one ball from bag B, what is the probability of selecting the ball labeled as 2 in the second draw?

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