
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 $EF = 12$. Find the length of the shorter angle trisector from $F$ to the hypotenuse $DF$.
A) $\frac{48\sqrt{3}}{17}$
B) $\frac{96\sqrt{3}}{17}$
C) $\frac{384\sqrt{3}}{17}$
D) $\frac{192\sqrt{3}}{17}$

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