
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 3 white balls and 4 red balls, while in bag B, there is 1 white ball and 2 red balls. Now, one ball is randomly taken from bag A and put into bag B, then two balls are randomly taken from bag B. What is the probability that all the balls taken out are red?

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