
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 9 red balls and 6 yellow balls. These balls are identical except for their colors. After thoroughly mixing the balls in the bag, one ball is randomly drawn.<br/>$(1)$ What is the probability of drawing a red ball? What is the probability of drawing a yellow ball?<br/>$(2)$ In order to make the probabilities of drawing a red ball and a yellow ball equal, 7 more balls are added to the bag. What should be the number of red and yellow balls among these 7 balls?

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