
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 $DEF$, the hypotenuse $\overline{DE}=13$ and leg $\overline{DF}=5$. The bisector of angle $D$ meets the opposite side in $D_1$. Another right triangle $XYZ$ is then constructed with hypotenuse $\overline{XY}=D_1E$ and leg $\overline{XZ}=D_1F$. If the bisector of angle $X$ meets the opposite side in $X_1$, the length of $XX_1$ is:
A) 0
B) 2
C) 4
D) 6
E) 8

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