
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 10 points marked on a circle. Any three of them form three inscribed angles. Petya counted the number of different values these angles could take. What is the maximum number he could have obtained?

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