
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
A shooter practices shooting, firing one bullet at a time, with every 5 shots considered a set. The practice for a set stops once a hit is achieved, and then moves on to the next set; otherwise, the shooter continues until all 5 bullets are fired before moving on to the next set. It is known that the hit rate for each shot is 0.8, and the outcomes of the shots are independent of each other.  
(I) Find the distribution of the number of bullets $\xi$ used in a set of practice and calculate the mathematical expectation of $\xi$;  
(II) Calculate the probability that exactly 4 bullets are used in total after completing two consecutive sets of practice.

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