
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
Bag X has 4 white marbles and 5 black marbles. Bag Y has 7 yellow marbles and 3 blue marbles. Bag Z has 3 yellow marbles and 6 blue marbles. A marble is drawn at random from Bag X. If it is white, a marble is drawn at random from Bag Y, otherwise, if it is black, a marble is drawn at random from Bag Z. What is the probability that the second marble drawn is yellow?

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