
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 lights along a road. If one of them goes out and the neighboring ones are still lit, the road service does not worry. But if two lights go out consecutively, the road service immediately replaces all the burnt-out lights.

Each light burns out independently of the others.

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

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

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