
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 $7$ black balls, all of which are identical except for their colors.  
$(1)$ If a ball is randomly drawn from the bag, the probability of drawing a ______ ball is higher.  
$(2)$ If an additional $6$ balls, consisting of red and black balls, are added to the bag, how should they be added to make the probabilities of drawing a red ball and a black ball equal?

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