
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, and the neighboring ones are still lit, then the road service is not concerned. However, if two consecutive streetlights burn out, the road service immediately replaces all the burnt out lights. Each streetlight burns out independently of the others.

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

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

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