
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
Given a triangle with side lengths 9 cm, 40 cm, and 41 cm, find the area. If this area is part of a larger square's surface, calculate what fraction of the square's total area this triangle covers, given that the side length of the square is 41 cm.

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