
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
A theater box office sells $2n$ tickets at 5 cents each, with each person limited to buying one ticket. Initially, the box office has no money, and among the first $2n$ people in line, half have 5 cent coins while the other half only have one dollar bills. How many different ways can these $2n$ ticket buyers line up so that the box office does not experience any difficulty in providing change?

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