
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
Points $F$, $H$, and $L$ are the midpoints of the sides of right triangle $BIM$. Points $N$, $P$, and $Q$ are the midpoints of triangle $FIM$, which is one of the four smaller triangles formed, and so on. If this process of shading one of the resulting four smaller triangles in each step is performed 50 times and the sides of triangle $BIM$ are $BM = MI = 12$ units, what is the total area of the shaded triangles if the shaded regions' process stops after 50 iterations?
A) 22 square units
B) 24 square units
C) 26 square units
D) 28 square units
E) 30 square units

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