
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 5 red balls and 10 yellow balls. All the balls are identical except for their colors. After thoroughly mixing the balls in the bag, one ball is randomly drawn.  
$(1)$ Find the probability of drawing a red ball.  
$(2)$ In order to make the probabilities of drawing the two types of balls equal, 9 more identical red or yellow balls are added. What should be the respective numbers of red and yellow balls among these 9 balls?

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