
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 now expanded his field, which remains a right triangle. The lengths of the legs of this field are $5$ units and $12$ units, respectively. He leaves an unplanted rectangular area $R$ in the corner where the two legs meet at a right angle. This rectangle has dimensions such that its shorter side runs along the leg of length $5$ units. The shortest distance from the rectangle $R$ to the hypotenuse is $3$ units. Find the fraction of the field that is planted.
A) $\frac{151}{200}$
B) $\frac{148}{200}$
C) $\frac{155}{200}$
D) $\frac{160}{200}$

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