
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 Farmer Pythagoras has a field in the shape of a right triangle with legs measuring $5$ and $12$ units. At the right angle, he designates a smaller unplanted right triangle whose legs running along the field's legs are of equal length. The shortest distance from the base of this small unplanted triangle to the hypotenuse of the field is $3$ units. Calculate the fraction of the right triangle field that is planted.

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