
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 PQR where PQ = PR = 10 units, a similar process of dividing the triangle by joining the midpoints and shading one of the resulting triangles is repeated. If this process is done 100 times, calculate the total area of all shaded triangles.

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