
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
A unit equilateral triangle is given. Divide each side into three equal parts. Remove the equilateral triangles whose bases are middle one-third segments. Now we have a new polygon. Remove the equilateral triangles whose bases are middle one-third segments of the sides of the polygon. After repeating these steps for infinite times, find the area of the new shape.

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