
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 2 and contains the point \(A\). Segment \(AB\) is tangent to the circle at \(A\) and \(\angle AOB = 2\theta\). If point \(C\) lies on \(\overline{OA}\) and \(\overline{BC}\) bisects \(\angle ABO\), then 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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