
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 5 black marbles. Bag B has 8 yellow marbles and 7 blue marbles. Bag C has 3 yellow marbles and 7 blue marbles. Bag D has 4 red marbles and 6 green marbles. A marble is drawn at random from Bag A. If it is white, a marble is drawn at random from Bag B; if it is black, a marble is drawn from Bag C. After drawing from Bag B or C, a marble is then drawn from Bag D. What is the probability that the second marble drawn is yellow, and the third marble drawn is green?

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