
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 bag A, there are 4 white balls and 6 black balls. In bag B, there are 4 white balls and 5 black balls. First, one ball is randomly taken from bag A and placed into bag B. Then, one ball is randomly taken from bag B. The probability of drawing a white ball from bag B under the condition that a white ball is drawn from bag A is ____.

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