
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
On the occasion of the start of winter holidays, all the boys from class 8 "B" went to a shooting range. It is known that there are $n$ boys in class 8 "B". At the shooting range, there are also $n$ targets. Each boy randomly chooses a target, and some boys might choose the same target. After that, all the boys simultaneously shoot at their chosen targets. It is known that every boy hits their target. A target is considered hit if at least one boy shot at it.

a) Find the expected number of hit targets.

b) Can the expected number of hit targets be less than $n / 2$?


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