
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 Dyck path of length \(2n\) is a path starting from the point \((0,0)\) in the plane and ending at the point \((2n, 0)\), taking steps either north-east or south-east (moving 1 unit to the right and 1 unit vertically) without ever passing below the x-axis. How many Dyck paths of length \(2n\) are there?

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