
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
Points  $ K$ ,  $ L$ ,  $ M$ , and  $ N$  lie in the plane of the square  $ ABCD$  so that  $ AKB$ ,  $ BLC$ ,  $ CMD$ , and  $ DNA$  are equilateral triangles. If  $ ABCD$  has an area of  $ 16$ , find the area of  $ KLMN$.

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