
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 radius 10 is tangent to all sides of a triangle which has one side of length 20 and two sides of length 13 each. Find the distance from the center of the sphere, O, to the plane containing the triangle.

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