
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 that there are 3 white balls and 2 red balls in bag A, and 2 white balls and 2 red balls in bag B, two balls are randomly taken from bag A and placed into bag B, then two balls are randomly taken from bag B, determine the probability that two white balls are taken from bag A, given that two white balls are taken from bag B.

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