
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 red, yellow, and white balls. Apart from their colors, all the balls are identical. There are $10$ red balls, $6$ yellow balls, and $4$ white balls in the bag. The balls are mixed in the bag.<br/>$(1)$ Randomly pick $1$ ball from the bag, find the probability of picking a white ball;<br/>$(2)$ Randomly pick $1$ ball from the bag, find the probability of picking a yellow or red ball;<br/>$(3)$ If $2$ red balls and $2$ white balls are first taken out from the bag and placed on the table, and then $1$ ball is randomly picked from the bag, find the probability of picking a white ball at this point.

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