
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 ball is placed inside a regular tetrahedron with each edge measuring 4 units, which is lying on a horizontal surface. Water is poured into the tetrahedron from the top, causing the ball to slowly float upwards. When the volume of the water reaches $\frac{7}{8}$ of the volume of the tetrahedron, the ball just touches each of the tetrahedron’s side faces and the water surface (with the ball completely floating above the water surface). Determine the surface area of the ball.

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