
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
a) There are 3 initially empty urns. One of them is chosen randomly with equal probability (1/3 for each). Then, a ball is placed inside the chosen urn. This process is repeated until one urn contains two balls. What is the probability that when the process ends, the total number of balls inside all the urns is 2?

b) Now, there are 2014 initially empty urns. Repeating the same process as before, what is the probability that in the end there are exactly 10 balls inside the urns?

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