
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. A triangle with sides of length 13, 13, and 10 is situated in space so that each of its sides is tangent to the sphere. Find the distance between O and the plane determined by the triangle.

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