
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
Thirteen distinct points are identified on the circumference of a circle with radius \( r \). How many different triangles can be formed if each vertex must be one of these 13 points and none of the sides of the triangles can be equal to the radius \( r \)?

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