
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 a total of 12 balls that are identical in shape and mass, including red, black, yellow, and green balls. When drawing a ball at random, the probability of getting a red ball is $\dfrac{1}{3}$, the probability of getting a black or yellow ball is $\dfrac{5}{12}$, and the probability of getting a yellow or green ball is also $\dfrac{5}{12}$.  
(1) Please calculate the probabilities of getting a black ball, a yellow ball, and a green ball, respectively;  
(2) When drawing a ball at random, calculate the probability of not getting a "red or green ball".

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