
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
The sphere with center \(O\) has a radius \(8\). There exists an isosceles triangle with sides \(13, 13,\) and \(10\) such that each side is tangent to the sphere. Determine the distance from \(O\) to the plane containing this triangle.
A) \(\frac{2\sqrt{119}}{3}\)
B) \(\frac{5\sqrt{3}}{3}\)
C) \(\frac{10\sqrt{3}}{3}\)
D) \(\frac{2\sqrt{3}}{3}\)

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