
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
Let the axial section of an inverted truncated cone-shaped container be an equilateral triangle. Water is poured into this container, and a solid sphere with radius \( r \) is placed inside. The sphere is tangent to the container walls and the water surface. What is the height of the water surface after the sphere is removed?

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