
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 Farmer Delta's field shaped as a right triangle, the lengths of the legs are $5$ and $12$ units respectively. In the corner where these sides meet at a right angle, there is a small unplanted square plot $P$ to give an artistic touch. The side length of square $P$ is equal to the shortest distance from $P$ to the hypotenuse. If the shortest distance from $P$ to the hypotenuse is $5/3$ units, what fraction of Delta's field is unplanted?
A) $\frac{5}{54}$  
B) $\frac{1}{45}$  
C) $\frac{1}{60}$  
D) $\frac{1}{54}$  
E) $\frac{4}{54}$

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