
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 car must pass through 4 intersections during its journey. At each intersection, the probability of encountering a green light (allowing passage) is $\frac{3}{4}$, and the probability of encountering a red light (stopping) is $\frac{1}{4}$. Assuming that the car only stops when it encounters a red light or reaches its destination, and letting $\xi$ represent the number of intersections passed when the car stops, find: (I) the probability distribution and expectation $E(\xi)$ of $\xi$; (II) the probability that at most 3 intersections have been passed when the car stops.

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