
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 sphere with center $O$ has a radius of $5$. An isosceles triangle with sides of length $13, 13,$ and $10$ is situated in space so that each of its sides is tangent to the sphere. Calculate the distance from $O$ to the plane determined by the triangle.
**A)** $\frac{5\sqrt{5}}{3}$
**B)** $\frac{10}{3}$
**C)** $\frac{5\sqrt{3}}{3}$
**D)** $5\sqrt{2}$

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