
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 8 white balls and 12 red balls, with each ball being identical except for color.  
$(1)$ The event of "drawing a yellow ball from the bag" is a ______ event. The probability of the event "drawing at least one red ball out of 9 balls drawn at once" occurring is ______.  
$(2)$ Find the probability of drawing a red ball from the bag at random.  
$(3)$ After removing x red balls from the bag and adding x white balls, and thoroughly mixing, if the probability of drawing a white ball at random is $\frac{4}{5}$, find the value of x.

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