
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-angled triangle, $CC_1$ its angle bisector, and $O$ the circumcenter. The intersection point of the line $OC_1$ with the perpendicular dropped from vertex $C$ onto side $AB$ lies on the circumcircle $\Omega$ of triangle $AOB$. Find angle $C$.

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