
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
From the vertices of a regular $n$-gon $(n \geqslant 6)$, two sets of three distinct points are chosen at random. What is the probability that the two triangles formed by these chosen sets of points do not intersect?

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