
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 roots of the equation $(z - 2)^6 = 64$ are mapped in the complex plane, and these points form a regular hexagon. If three of the vertices of this hexagon are labeled $D, E,$ and $F$, compute the least possible area of triangle $DEF$.

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