
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
The ticket price for a concert is 50 yuan. Among the customers in line to buy tickets, $n$ of them have a 50-yuan bill, and $m$ of them have a 100-yuan bill. The ticket office has no 50-yuan change initially. How many ways are there to arrange the queue so that each purchase can be processed smoothly without running out of change? Assume that each customer is limited to buying one ticket, and $n \geqslant m$.

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