
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 1996 points on a circle, and they are painted in several different colors. From each set of points of the same color, one point is selected to form an inscribed polygon whose vertices are all of different colors. If the number of points of each color is different, into how many different colors should the 1996 points be painted to maximize the number of such polygons? And how many points should each color have?

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