
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
The following experiment is conducted. In a room, there are two identical-looking urns. The left one contains $a$ balls, and the right one contains $b$ balls. People enter the room one by one, and each transfers a ball from the left urn to the right urn or from the right urn to the left urn. It is assumed that the probability of transferring a ball from the left urn to the right urn is equal to the probability of transferring a ball from the right urn to the left urn, which is $\frac{1}{2}$. The experiment continues until one of the urns is empty. What is the probability that the left urn is emptied? What is the probability that the right urn is emptied? What is the probability that the experiment never ends?

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