
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 $A$, with $\angle AOB=\theta$. If point $C$ lies on $\overline{OA}$ and point $D$ also on $\overline{OA}$ such that $\overline{BD}$ is the angle bisector of $\angle ABO$, then express $OD$ 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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