
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
6. Three targets. A shooter fires at three targets until all are hit. The probability of hitting a target with a single shot is \( p \). 

a) Find the probability that exactly 5 shots are needed.

b) Find the expected number of shots needed.

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