
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 $r$ balls labeled from 1 to $r$ and $n$ boxes labeled from 1 to $n$, with $r \geq n$. The balls are placed into the boxes, with each box having an unlimited capacity. Find the number of ways to place the balls such that no box is empty, denoted as $f(r, n)$. Additionally, if the $n$ boxes are unlabeled and indistinguishable, still find the number of ways to place the balls such that no box is empty, denoted as $s(r, n)$.

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