
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 square has a side length of 2 and an inscribed circle centered at $O$ with radius 1. Point $A$ is a point of tangency between the circle and the square, and point $B$ lies outside the square such that segment $AB$ is tangent at $A$. If $\angle AOB = 2\theta$ and point $C$ lies on $\overline{OA}$ with $\overline{BC}$ bisecting $\angle ABO$, express $OC$ in terms of $s = \sin 2\theta$ and $c = \cos 2\theta$.

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