
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 8 balls of identical shape and size, including 5 red balls and 3 white balls. A person draws a ball from the bag one by one. For the first draw, they take out a ball, note its color, and then put it back in the bag. For the second draw, they take out a ball, note its color, and do not put it back in the bag. For the third draw, they take out a ball, note its color, and put it back in the bag. For the fourth draw, they take out a ball, note its color, and do not put it back in the bag. This process continues until all balls are drawn.  
(1) Calculate the probability of drawing a red ball exactly on the fourth draw;  
(2) Let $\xi$ denote the number of red balls drawn in the first three draws. Write down its distribution and calculate the expectation $E\xi$.

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