
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 street lamps along a road. If one lamp burns out while the neighboring lamps are still lit, the road service does not take action. However, if two adjacent lamps burn out, the road service immediately replaces all the burnt-out lamps. Each lamp burns out independently of the others.

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

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

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