
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
Sixty points, of which thirty are coloured red, twenty are coloured blue and ten are coloured green, are marked on a circle. These points divide the circle into sixty arcs. Each of these arcs is assigned a number according to the colours of its endpoints: an arc between a red and a green point is assigned a number  $1$ , an arc between a red and a blue point is assigned a number  $2$ , and an arc between a blue and a green point is assigned a number  $3$ . The arcs between two points of the same colour are assigned a number  $0$ . What is the greatest possible sum of all the numbers assigned to the arcs?

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