
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 right triangle $DEF$ where the hypotenuse $\overline{DE}=13$ and leg $\overline{DF}=12$, find the point $D_1$ where the bisector of angle $D$ meets the opposite side $\overline{EF}$. Construct a new right triangle $XYZ$ with hypotenuse $\overline{XY} = D_1E$ and leg $\overline{XZ} = D_1F$. Calculate the length of $XX_1$, where $X_1$ is the point where the bisector of angle $X$ meets side $\overline{YZ}$.
A) $\frac{12}{15}$
B) $\frac{12}{25}$
C) $\frac{13}{25}$
D) $\frac{12}{30}$
E) $\frac{12}{5}$

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