
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
Let  $ ABC$  be an acute triangle,  $ CC_1$  its bisector,  $ O$  its circumcenter. The perpendicular from  $ C$  to  $ AB$  meets line  $ OC_1$  in a point lying on the circumcircle of  $ AOB$ . Determine angle  $ C$ .

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