
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
Nine distinct points are placed on the circumference of a circle such that no three points are collinear along any line that passes through the circle's center. How many different triangles can be formed if each vertex must be one of these 9 points, and additionally, how many distinct straight lines can be drawn connecting pairs of these points?

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