
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 40 red points, 30 blue points, and 20 green points evenly distributed on the circumference of a circle, which is divided into 90 arcs. Each arc is labeled with a number based on the colors of its endpoints: an arc between a red and blue point is labeled 1; between a red and green point, 2; and between a blue and green point, 3. An arc with endpoints of the same color is labeled 0. Find the maximum and minimum possible values of the sum of all labels.

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