
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 regular tetrahedron with each edge length of $4$, there is a small ball $O$ (ignore its weight) inside. Water is poured into the tetrahedron from the top, causing the ball to float upwards. When the volume of the poured water is $\frac{7}{8}$ of the tetrahedron's volume, the ball is tangent to all the tetrahedron's side faces and the water surface. Calculate the surface area of the ball.

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