
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
Consider a right triangle $PQR$ with $PQ = QR = 8$. This triangle undergoes a process where it is split into four smaller right triangles by joining the midpoints of its sides, and in each division, the right triangle at the hypotenuse's opposite vertex is shaded. If this process is repeated for 100 cycles, determine the total area of all shaded triangles.

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