
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 $2n$ people lined up at a theater box office to buy tickets. Among them, $n$ people each have a 5-cent bill and $n$ people each have a 1-yuan bill. Each person wants to buy a ticket that costs 5 cents, but the box office starts with no change. How many ways can the people line up so that the process goes smoothly without encountering a situation where there is no change available?

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