
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 two identical urns. The first urn contains 3 black balls and 7 white balls, and the second urn contains 4 black balls and 6 white balls. One urn is randomly chosen, and one ball is randomly drawn from it, which turns out to be white. What is the probability that this white ball was drawn from the first urn?

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