
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
In the beautiful city of Perpignan, a gardener is decorating a circular park on the edge of which there are $2n$ gates. He wants to draw $n$ paths linking each pair of gates, such that each gate is connected to another and no two paths intersect. In how many ways can he proceed?

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