
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
A rocket artillery system of a missile cruiser fires at a target. If the target is not hit, the system automatically fires a second shot at the same target. A third shot at this target is not made. The cruiser has 10 rockets on board. During exercises, it fires at several targets under identical conditions. The probability of hitting a target with a single shot is $p$.

a) If there are five targets, what is the probability that exactly three unused rockets remain after the firing?

b) Find the expected number of targets hit if there are nine targets.

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