
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
Triangle $ABC$ is equilateral with side length $10$. Point $O$ is the center of the inscribed circle of this triangle. Calculate the area of the circle passing through points $A$, $O$, and $C$.
**A)** $90\pi\qquad$ **B)** $100\pi\qquad$ **C)** $\frac{100\pi}{3}\qquad$ **D)** $\frac{300\pi}{9}\qquad$ **E)** $\frac{90\pi}{3}$

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