
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
In a bag, there are 12 balls, which are red, black, yellow, and green. When drawing a ball at random, the probability of getting a red ball is $\frac{1}{3}$, the probability of getting either a black or a yellow ball is $\frac{5}{12}$, and the probability of getting either a yellow or a green ball is also $\frac{5}{12}$. What are the probabilities of getting a black ball, a yellow ball, and a green ball, respectively?

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