
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 $12$ red balls and $6$ white balls, all of which are identical except for color. After thorough mixing, a ball is randomly drawn from the bag.  
$(1)$ What is the probability of drawing a red ball?  
$(2)$ If some red balls are taken out from the bag, then after thorough mixing and randomly drawing a ball, the probability of drawing a white ball is $\frac{2}{5}$. How many red balls were taken out?

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