
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
Containers X, Y, and Z are arranged such that:
- Container X holds 3 red balls and 7 green balls.
- Container Y holds 8 red balls and 2 green balls.
- Container Z holds 5 red balls and 5 green balls.
A container is chosen at random, and subsequently, one ball is selected from that chosen container. What is the probability that the ball is green?

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