
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 $8$. An isosceles triangle with sides $13, 13,$ and $10$ is positioned such that each side is tangent to the sphere. Determine the distance between point $O$ and the plane containing the triangle.
A) $\frac{20\sqrt{7}}{3}$
B) $4\sqrt{6}$
C) $8$
D) $7$
E) $6\sqrt{3}$

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