
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 an opaque bag, there are only $12$ balls with different colors, including $4$ red balls and $8$ black balls. <br/>$(1)$ First, $m\left(m \gt 1\right)$ red balls are taken out of the bag, and then $1$ ball is randomly drawn from the bag. Let "drawing a black ball" be event $A$. Please complete the following table:

| Event $A$ | Certain Event | Random Event |
|-----------|---------------|--------------|
| $m$ value | ______        | ______       |

$(2)$ $n$ red balls are taken out of the bag and mixed, the probability of drawing a black ball is $\frac{8}{9}$. Find the value of $n$.

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