
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 dark box, there are 6 black balls and 4 white balls.  
(1) Take out 3 balls in sequence without replacement. If the first ball taken out is white, find the probability of getting a black ball on the third draw;  
(2) Take out 3 balls in sequence with replacement. If the first ball taken out is white, find the probability of getting a black ball on the third draw;  
(3) Take out 3 balls in sequence with replacement. Find the distribution and expectation of the number of white balls drawn, denoted as $\xi$.

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