
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 Euler has a field in the form of a right triangle with its legs measuring $5$ units and $12$ units. He plants the entire field except for a small square plot $S$ located at the right angle. This square has one of its vertices at the right angle vertex of the triangle. The nearest distance from square $S$ to the hypotenuse is $3$ units. Determine the fraction of the field that is planted.

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