
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, where AB=6, BC=8, and CA=10. Then:  
(1) The distance from the center of the sphere to plane ABC is \_\_\_\_ ;  
(2) The tangent of the acute angle formed by the great circle passing through points A and B and plane ABC is \_\_\_ .

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