
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 X holds 5 red balls and 5 green balls; container Y holds 7 red balls and 3 green balls; container Z holds 2 red balls and 8 green balls. A container is selected such that the probability of picking each is as follows: $P(X) = 0.2$, $P(Y) = 0.5$, and $P(Z) = 0.3$. After choosing a container, a ball is randomly selected from that container. Calculate the probability of selecting a green ball.

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