
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 tetrahedron ABCD where each vertex lies on the surface of sphere O, with AB=AC=5, BC=8, and AD⊥ to the base ABC. Let G be the centroid of triangle ABC, and the tangent of the angle formed by line DG and the base ABC is $\frac{1}{2}$. Find the surface area of sphere O.

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