
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 triangle $XYZ$, $XY=130$, $XZ=113$, and $YZ=118$. The angle bisector of angle $X$ intersects $\overline{YZ}$ at point $D$, and the angle bisector of angle $Y$ intersects $\overline{XZ}$ at point $E$. Let $G$ and $H$ be the feet of the perpendiculars from $Z$ to $\overline{YE}$ and $\overline{XD}$, respectively. Find $GH$.

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