
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
There are 1989 points in space, none of which are collinear. These points are divided into 30 groups with different numbers of points in each group. From each of three different groups, one point is taken to form a triangle. To maximize the total number of triangles, how many points should each group contain?

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