
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 12 urns: in 6 urns (composition $A_{1}$) there are 3 white and 4 black balls, in 3 urns (composition $A_{2}$) there are 2 white and 8 black balls, in 2 urns (composition $A_{3}$) there are 6 white and 1 black ball, and in 1 urn (composition $A_{4}$) there are 4 white and 3 black balls. A ball is drawn from a randomly selected urn. What is the probability that the ball was drawn from an urn of composition $A_{3}$, given that it is white?

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