
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 circumference is divided into 90 arc segments, and each arc segment is assigned a number based on the colors of its end points: a red-blue arc is labeled 1, a red-green arc is labeled 2, a blue-green arc is labeled 3, and an arc where both end points are the same color is labeled 0. Find the maximum and minimum possible sum of all the numbers assigned to the arc segments.

(2016, National Junior High School Mathematics Invitational Competition)

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