
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
There are three urns with balls. The first urn contains 4 white and 5 black balls, the second contains 5 white and 4 black balls, and the third contains 6 white balls. A person randomly selects one of the urns and extracts a ball. Find the probability that: a) the ball is white; b) the white ball was drawn from the second urn.

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