
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
Two distinct points \( A \) and \( B \) are given strictly inside a circle. Where on the circle should point \( C \) be located so that the angle \( \angle ACB \) is as large as possible? Indicate all possibilities and justify that there are no other options.

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