
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 red marbles and 5 green marbles. Bag B has 8 purple marbles and 2 orange marbles. Bag C has 3 purple marbles and 7 orange marbles. Bag D has 4 purple marbles and 6 orange marbles. A marble is drawn at random from Bag A. If it is red, a marble is drawn at random from Bag B; if it is green, a marble is drawn at random from Bag C, but if it is neither (an impossible scenario in this setup), a marble would be drawn from Bag D. What is the probability that the second marble drawn is purple?

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