
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 entirely painted blue. Each iteration, the middle ninth of each blue region turns green. After three iterations, what fractional part of the original area of the blue triangle remains blue.

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