
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 that is fully painted blue, each time a transformation occurs one quarter of the middle area of each blue square turns red. After three transformations, determine the fraction of the original area of the square that remains blue.

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