
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
A circle centered at \( O \) has radius 1 and contains the point \( A \). Segment \( AB \) is tangent to the circle at \( A \) and \( \angle AOB = 2\theta \). If point \( C \) lies on \( \overline{OA} \) such that \( OC = \frac{3}{4} OA \) and \( \overline{BC} \) bisects \( \angle ABO \), express \( OC \) in terms of \( s \) and \( c \), where \( s = \sin(2\theta) \) and \( c = \cos(2\theta) \).

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