
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 obtuse triangle with circumcenter \(O\) such that \(\angle ABC = 15^\circ\) and \(\angle BAC > 90^\circ\). Suppose that \(AO\) meets \(BC\) at \(D\), and that \(OD^2 + OC \cdot DC = OC^2\). Find \(\angle C\).

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