
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 a right-angled triangle field, the lengths of the legs are 5 units and 12 units. At the vertex where these two sides meet at a right angle, Farmer Euclid plans to leave a small unplanted square patch. The rest of the field is planted. The shortest distance from the square to the hypotenuse is 3 units. What fraction of the field is planted?
A) $\frac{85612}{85683}$
B) $\frac{85611}{85682}$
C) $\frac{85610}{85683}$
D) $\frac{85611}{85683}$

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