
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 that Farmer Pythagoras's right triangle has legs of lengths $5$ units and $12$ units, he plants two different crops, dividing the field into two right triangles by a line parallel to one of the legs starting from the right angle vertex. The smaller triangle near the vertex is unplanted and is used for a decorative square garden $S$ which shares one vertex with the field's right angle. The shortest distance from the corner of square $S$ opposite the right angle to the hypotenuse is $3$ units. Find the fraction of the field that is planted with crops.

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