
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 Pythagoras has expanded his field to a larger right triangle shape with legs of lengths $5$ units and $12$ units. He still leaves a small unplanted square $S$ in the same corner where the legs meet at a right angle. The shortest distance from $S$ to the hypotenuse is now $4$ units. Calculate the fraction of the field that is planted.

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