
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 with center $O$ and radius 1 contains point $A$. Segment $AB$ is tangent to the circle at $A$ and $\angle AOB = \theta$. A second circle with center $B$ and radius $r \sin \theta$ is tangent to segment $AB$ at $B$. If point $C$ lies on $\overline{OA}$ and $\overline{BC}$ bisects $\angle ABO$, express $OC$ in terms of $s = \sin \theta$, $c = \cos \theta$, and $r$.

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