
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
Given a sphere with a section of the sphere forming a triangle with vertices A, B, and C, where AB=6, BC=8, and AC=10, find the surface area of the sphere, given that the distance from the center of the sphere to this section is half of the sphere's radius.

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