
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
Place $n$ distinct balls into $r$ boxes ($n \geqslant r$) with no restrictions on the number of balls per box. Find the number of ways to place the balls in the following scenarios under the condition that there are no empty boxes:
(1) The $r$ boxes are distinguishable (identifiable).
(2) The $r$ boxes are indistinguishable (non-identifiable).

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