
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
Given \( n \in \mathbb{N}^{*} \), there are \( 2n \) points on the circumference of a circle. Let \( F_n \) be the number of ways to connect these points in pairs using \( n \) non-intersecting chords inside the circle. Find a recurrence relation for \( F_n \).

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