
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 square sheet of paper has each of its four corners folded into smaller isosceles right triangles which are then cut out. If the side length $AB$ of the original square is $16$ units, and each corner triangle is made from folds such that the legs of the triangles are equal to half the side length of smaller squares formed inside the original square, calculate the total area of the four triangles removed.

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