
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
In a right triangle ABC with AB = 6 and BC = 8, points D, E, and F are midpoints of the sides. Points G, H, and I are midpoints of the sides of triangle DEF, etc. If this dividing and shading process is done 100 times and in each iteration, the triangle opposite the right angle is shaded, determine the total area of the shaded triangles.

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