
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 $20$ identical balls except for their colors, with $5$ red balls and $15$ yellow balls. <br/>$(1)$ Drawing a ball randomly from the bag, the probability of drawing a ______ ball is small; <br/>$(2)$ If a ball is drawn randomly from the bag, the probability of drawing a yellow ball is ______; <br/>$(3)$ If the probability of drawing a red ball randomly from the bag is $\frac{2}{3}$, then ______ more red balls need to be added to the bag; <br/>$(4)$ If an additional $20$ balls of the same type (red and yellow) are put into the bag, how should they be added to make the probability of drawing a red ball and a yellow ball the same? Please calculate the number of red and yellow balls to be added to the bag.

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