
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
An urn initially contains one white ball. Another ball, either white or black (with equal probabilities), is added to the urn. After that, a ball is randomly drawn from the urn, and it turns out to be white. What is the conditional probability that the remaining ball in the urn is also white?

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