
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
The base of the quadrilateral pyramid \( S M N K L \) is a rhombus \( M N K L \) with side length 4 and an acute angle \( N M K \) of \( 60^\circ \). It is known that \( S M = 2 \) and \( S N = 4 \). Determine the lengths of the remaining two edges \( S K \) and \( S L \) that maximize the volume of the pyramid, and calculate this volume.

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