
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 right triangle XYZ has legs XY = YZ = 8 cm. In each step of an iterative process, the triangle is divided into four smaller right triangles by joining the midpoints of the sides. However, for this problem, the area of the shaded triangle in each iteration is reduced by a factor of 3 rather than 4. If this process is repeated indefinitely, calculate the total area of the shaded triangles.

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