
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 on a circle. The circle is divided into 90 arcs. For each arc, a number is assigned based on the colors of the endpoints: 1 if one endpoint is red and the other is blue, 2 if one endpoint is red and the other is green, 3 if one endpoint is blue and the other is green, and 0 if both endpoints are of the same color. Find the maximum and minimum possible values of the sum of all the numbers assigned to the arcs.

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