
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 a radius of 2 and contains point $A$. Segments $AB$ and $AD$ are tangents to the circle at points $A$ and $D$, respectively, with $A \neq D$ and $\angle AOB=\theta$. Point $C$ lies on line $\overline{OA}$ and line segment $\overline{BC}$ bisects $\angle ABO$. If $\angle AOD = 2\theta$, express $OC$ in terms of $s$ and $c,$ where $s = \sin \theta$ and $c = \cos \theta$.

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