
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 box, there are a total of 30 small balls of three colors: red, yellow, and blue. Apart from the colors, all other characteristics of the balls are the same. There are 6 red balls, and the number of yellow balls is twice the number of blue balls.  
$(1)$ Find the probability of drawing a blue ball.  
$(2)$ How many additional blue balls need to be added to the box to make the probability of drawing a blue ball $\frac{1}{2}$?

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