
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
There are two sets of containers. Set 1 includes Container A holding 2 red balls and 8 green balls; Containers B and C each hold 8 red balls and 2 green balls. Set 2 includes Container A holding 8 red and 2 green balls, and Containers B and C each holding 2 red and 8 green balls. A fair coin is flipped to determine which set of containers will be used. A container within that set is then randomly selected and a single ball is then drawn from the selected container. Calculate the probability that the ball drawn is green. Express your answer as a common fraction.

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