
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
Points $A$ and $C$ are on a circle centered at $O$, each of $\overline{BA}$ and $\overline{BC}$ are tangent to the circle, and $\triangle ABC$ is an isosceles right triangle with $\angle ACB = 90^\circ$. The circle intersects $\overline{BO}$ at $D$. Determine $\frac{BD}{BO}$.
A) $1 - \frac{\sqrt{2} + \sqrt{6}}{4} \qquad$ B) $\frac{1}{2} \qquad$ C) $\frac{\sqrt{2}}{2} \qquad$ D) $\frac{\sqrt{3}}{2} \qquad$ E) $\frac{\sqrt{6}}{6}$

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