
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
Juquinha marks points on the circumference and draws triangles by connecting 3 of these points. The lengths of the arcs between 2 consecutive points are equal.

a) By marking 4 points on the circumference, how many triangles can he draw?

b) By marking 5 points on the circumference, how many equilateral triangles can he draw?

c) How many right triangles can he draw if he marks 6 points?

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