
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
An equilateral triangle is painted entirely black. During each transformation, one third of each currently black triangle turns white. After six transformations, what fraction of the original area of the black triangle remains black?
A) $\frac{64}{729}$
B) $\frac{128}{729}$
C) $\frac{32}{243}$
D) $\frac{256}{6561}$
E) $\frac{1}{3}$

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