
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
Triangle $GHI$ has sides of length 6, 8, and 10 units (it's a right triangle), and triangle $JKL$ has sides with lengths 9, 40, and 41 units. Triangle $GHI$ has a perpendicular from $I$ to $GH$ at point $M$ which divides $GH$ into segments 3 units and 5 units in length. Calculate the ratio of the area of triangle $GHI$ to the triangle $JKL$.

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