
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
There are 9 streetlights along a road. If one of them burns out but the adjacent ones are still working, the road service does not worry. However, if two consecutive lights burn out, the road service immediately replaces all the burned-out lights. Each streetlight burns out independently of the others.

a) Find the probability that exactly 4 lights will need to be replaced during the next service.

b) Find the expected number of lights that will need to be replaced during the next service.

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