
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
Triangles in a circle. Suppose $n$ points on the circumference are connected to each other in all possible ways with straight lines, none of which intersect at the same interior point of the circle. Determine the number of triangles formed by these lines whose vertices all lie within the given circle.

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