
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 $XYZ$, the hypotenuse $\overline{XZ}=13$ and leg $\overline{XY}=5$. The bisector of angle $X$ meets the opposite side at $X_1$. A second right triangle $LMN$ is then constructed with hypotenuse $\overline{LM}=X_1Z$ and leg $\overline{LN}=X_1Y$. If the bisector of angle $L$ meets the opposite side at $L_1$, find the length of $LL_1$.
A) $\frac{21}{17}$
B) $\frac{20}{17}$
C) $\frac{22}{17}$
D) $\frac{23}{17}$

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