
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 right $\triangle DEF$ where $DE = 5$ and $EF = 12$, calculate the length of the shorter trisector of angle $E$ that intersects the hypotenuse $DF$.
A) $\frac{5}{36}$
B) $\frac{5\sqrt{3}}{36}$
C) $\frac{5\sqrt{2}}{36}$
D) $\frac{5\sqrt{5}}{36}$

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