
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
A bag contains $5$ red balls and $3$ white balls that are identical in shape and size.<br/>$(1)$ Find the probability of drawing exactly one white ball from the bag;<br/>$(2)$ If $n$ white balls, identical in shape and size to the balls in the bag, are added to the bag, and the probability of drawing exactly one red ball from the bag is $\frac{1}{2}$, find the value of $n$.

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