
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
Given a square initially painted black, with $\frac{1}{2}$ of the square black and the remaining part white, determine the fractional part of the original area of the black square that remains black after six changes where the middle fourth of each black area turns white.

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