
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
1. On a semicircle with AB as the diameter, besides points A and B, there are 6 other points. Since there are also 4 other points on AB, making a total of 12 points, how many quadrilaterals can be formed with these 12 points as vertices?
2. On one side of angle A, there are five points (excluding A), and on the other side, there are four points (excluding A). With these ten points (including A), how many triangles can be formed?
3. Suppose there are 3 equally spaced parallel lines intersecting with another set of 4 equally spaced parallel lines. How many triangles can be formed with these intersection points as vertices?

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