
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
Distribute $n$ identical (i.e., indistinguishable) soccer balls to $r$ soccer teams, such that each team receives at least $s_{1}$ soccer balls, but at most $s_{2}$ soccer balls $\left(r s_{1} \leqslant n \leqslant r s_{2}\right)$. How many different ways are there to do this?

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