
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
40 red, 30 blue, and 20 green points are marked on a circle. A number is placed on each arc between neighboring red and blue points (1), red and green points (2), and blue and green points (3). (On arcs between points of the same color, 0 is placed.) Find the maximum possible sum of the placed numbers.

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