
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
Ten distinct points are placed on the circumference of a circle. How many different triangles can be formed if each vertex must be one of these 10 points, and no side of the triangles can subtend an arc greater than 180 degrees?

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