
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 $\angle AOB=\theta$. Point $C$ lies on $\overline{OA}$ such that $\overline{BC}$ bisects $\angle OBA$, and the length of $\overline{OA}$ is $r$. Express $OC$ in terms of $s$, $c$, and $r$ where $s = \sin \theta$, $c = \cos \theta,$ and $r = |OA|$.

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