
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 with sides of length 1 is divided by three lines parallel to its sides into four equal triangles, and the middle triangle is removed. Each of the remaining three triangles is then divided similarly into four equal parts, and their middle triangles are also removed. This process is repeated for each of the remaining triangles, and so on. Suppose this operation is repeated 12 times. How many equilateral triangles with side length \( \frac{1}{2^{12}} \) are left?

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