
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
On the surface of a sphere with a radius of 13, there are three points A, B, and C. The distance AB is 6, BC is 8, and CA is 10. Calculate the distance from the center of the sphere to the plane that includes points A, B, and C.

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