
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 village, a plot of land is shaped as a right triangle, where one of the legs measures 5 units and another measures 12 units. Farmer Euclid decides to leave a small unplanted square at the vertex of this right angle, and the shortest distance from this unplanted square to the hypotenuse is 3 units. Determine the fraction of the plot that is planted.
A) $\frac{412}{1000}$
B) $\frac{500}{1000}$
C) $\frac{290}{1000}$
D) $\frac{145}{1000}$
E) $\frac{873}{1000}$

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