
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 is originally painted blue, each time the square is changed, the middle ninth of each blue square turns red. After four changes, determine the fractional part of the original area of the blue square that remains blue.

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