
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 sphere with radius $R$. A point $S$ is located at a distance of $2R$ from the center of the sphere, and from this point, all tangent lines to the sphere are drawn (i.e., lines that have exactly one common point with the sphere). What does the set of these tangent lines represent? Calculate the surface area formed by the segments of the tangent lines from point $S$ to the points of tangency.

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