
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 $ABC$ with each side of length 10 is divided by joining the midpoints of each side, creating four smaller triangles. If this procedure is repeated 50 times, with the topmost triangle in each step being shaded, calculate the cumulative area of these shaded triangles.

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