
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 box, there are 8 identical balls, including 3 red balls, 4 white balls, and 1 black ball.  
$(1)$ If two balls are drawn consecutively without replacement from the box, one at a time, find the probability of drawing a red ball on the first draw and then drawing a red ball on the second draw.  
$(2)$ If three balls are drawn with replacement from the box, find the probability distribution and the expected value of the number of white balls drawn.

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