
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
An opaque bag contains $6$ red balls, $9$ yellow balls, and $3$ green balls. These balls have no other distinguishing features besides their colors. One ball is randomly drawn from the bag.  
$(1)$ Calculate the probability of drawing a green ball.  
$(2)$ If the probability of drawing a green ball is to be $\frac{1}{4}$, how many additional green balls need to be added to the bag?

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