
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
Farmer Geometria has a field in the shape of a right triangle. One leg of the triangle has a length of $5$ units and the other leg has $12$ units. She decides to leave a small unplanted square patch $S$ in the right-angled corner for aesthetic purposes. The shortest distance from the square $S$ to the hypotenuse is $3$ units. Find the fraction of the field that is planted.
A) $\frac{1458}{1470}$
B) $\frac{1460}{1470}$
C) $\frac{1461}{1470}$
D) $\frac{1462}{1470}$
E) $\frac{1463}{1470}$

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