
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 sphere with a surface area of $195.8 \mathrm{dm}^{2}$ is submerged to a depth of $1.2 \mathrm{dm}$ in water at $+4 \mathrm{C}$. What is the surface area of the submerged part, how much does the sphere weigh, and what is the vertex angle of the submerged spherical cap?

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