
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

Let \( n \) be a positive integer. Given \( 2n \) distinct points on a circle, we divide these points into \( n \) pairs and connect each pair with a directed line segment. A resulting graph is termed "good" if any two directed line segments do not intersect, and there does not exist directed line segments \(\overrightarrow{AB}\) and \(\overrightarrow{CD}\) such that the convex quadrilateral formed by \(A\), \(B\), \(C\), \(D\) as vertices arranged in clockwise order contains \(\overrightarrow{AB}\) and \(\overrightarrow{CD}\) as its two diagonals. How many good graphs are there?

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