
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
Given that the probability of a person making a basket in each shot is $p$, and the results of each shot are independent of each other, find the probability that there are exactly $r$ successful shots by the time the $n$th shot is taken.

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