
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]


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A regular tetrahedron with edge length 1 is given. A sphere touches three of its edges that emanate from one vertex, at their endpoints. Find the area of the part of the sphere’s surface that is located inside the tetrahedron.

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