
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 a bag, there are $4$ red balls and $2$ white balls of the same size. If $3$ balls are randomly drawn from the bag, the probability of exactly one white ball being drawn is ____. If $2$ balls are drawn without replacement for $2$ times, with each time drawing $1$ ball, and event $A$ is defined as "drawing a red ball on the first draw" and event $B$ is defined as "drawing a red ball on the second draw," then $P\left(B|A\right)=$ ____.

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