
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
A box contains $12$ balls, of which $5$ are red, $4$ are black, $2$ are white, and $1$ is green. A ball is randomly drawn from the box. Find:

$(1)$ the probability that the drawn ball is either red or black;

$(2)$ the probability that the drawn ball is not green.

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