
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 A has 5 white marbles and 6 black marbles. Bag B has 8 yellow marbles and 6 blue marbles. Bag C has 3 yellow marbles and 9 blue marbles. A marble is drawn at random from Bag A. If it is white, a marble is drawn at random from Bag B, otherwise, if it is black, a marble is drawn at random from Bag C. What is the probability that the second marble drawn is yellow?

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