
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 that points \( M \), \( N \), and \( K \) are located on the edges of a trihedral angle with vertex at point \( S \) such that \( SM^2 + SN^2 + SK^2 \leq 12 \). Find the area of triangle \( SMN \), given that the angle \( \angle MSN \) is \( 30^\circ \) and the volume of pyramid \( SMNK \) is maximized.

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