
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 solid spherical segment with a specific gravity of $s$ floats in water such that only the spherical cap associated with the segment is above water. What is the half-angle of the cone associated with the spherical segment? What is the condition for solvability? What is the half-angle if $s=0.75?$ (Half-angle: the angle between the generating line and the axis of rotation.)

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