
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 6 blue marbles. Bag C has 3 yellow marbles and 7 blue marbles. Bag D has 4 green marbles and 6 red marbles. A marble is drawn at random from Bag A. If it is white, a marble is drawn from Bag B, if it is black, a marble is drawn from Bag C. Furthermore, if a blue marble is drawn from Bag B, another marble is drawn from Bag B; if a blue marble is drawn from Bag C and the initial marble from Bag A was black, a marble is drawn from Bag D. What is the probability that the last marble drawn is yellow?

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