
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
Two bags \( U_{1} \) and \( U_{2} \) contain identical red and white balls. \( U_{1} \) contains \( A \) red balls and 2 white balls. \( U_{2} \) contains 2 red balls and \( B \) white balls. Take two balls out of each bag. If the probability that all four balls are red is \(\frac{1}{60}\), find the value of \( B \).

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