
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

19. Replacing streetlights. Along a road, there are 9 streetlights. If one streetlight fails but the adjacent ones are working, the road service does not take action. However, if two adjacent streetlights fail, the road service immediately replaces all failed streetlights. Each streetlight fails independently of the others.

a) Find the probability that during the next replacement exactly 4 streetlights need to be replaced.

b) Find the expected number of streetlights that need to be replaced during the next replacement.

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