
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
In a regular tetrahedron, points \( M \) and \( N \) are the midpoints of opposite edges. The orthogonal projection of the tetrahedron onto a plane parallel to line \( M N \) is a quadrilateral with area \( S \), one of whose angles is \( 60^\circ \). Find the surface area of the tetrahedron.

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