
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 originally painted black. Each time the triangle is changed, the middle ninth of each black triangle turns white. After three changes, what fractional part of the original area of the black triangle remains black.

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