
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
Bag A contains 2 red balls, 2 white balls, and 1 black ball, while bag B contains 3 red balls, 1 white ball, and 1 black ball. A ball is first randomly taken from bag A and placed into bag B. Then a ball is randomly taken from bag B. Express the probability that the ball drawn from bag B is red.

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