
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
Container I holds 8 red balls and 4 green balls; container II holds 3 red balls and 5 green balls; container III holds 4 red balls and 6 green balls. A container is randomly selected and then a ball is randomly selected from that container. What is the probability that the ball selected is green? Express your answer as a common fraction.

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