
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
Triangle $XYZ$ has $XY=17, YZ=18$ and $XZ=20$. Let $P$ be the point on line $\overline{XZ}$ such that $PZ=12$. There are exactly two points $D$ and $E$ on line $YP$ such that quadrilaterals $XYDZ$ and $XYEZ$ are trapezoids. Calculate the distance between points $D$ and $E$.

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