
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 of the lamps goes out, but the adjacent ones are still lit, maintenance does not worry. However, if two adjacent lamps go out, the maintenance service immediately replaces all burnt-out lamps. Each lamp burns out independently of the others.

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

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

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