
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 initially painted black. In each cycle of change, the middle third of each black region turns white. After three cycles of changes, what fraction of the original area of the black triangle remains black?
A) $\frac{8}{27}$ 
B) $\frac{1}{9}$
C) $\frac{16}{81}$
D) $\frac{4}{9}$
E) $\frac{1}{3}$

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