
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 $n$ boxes and $r$ balls. The balls are randomly distributed among the boxes. Find the probability that the $i$-th box contains $k$ balls, and the boxes with the numbers $1, 2, \ldots, i-1$ contain a total of $l$ balls $(k+l \leqslant r)$.

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