
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 a coordinate plane, triangle $XYZ$ has a right angle at $Y$, with $XY=5$ and $YZ=5$. Triangle $XZW$ has a right angle at $Z$, and $ZW=15$. $Y$ and $W$ are on opposite sides of line $XZ$. The line through $W$ parallel to $XY$ intersects line $YZ$ extended at point $V$. If
\[
\frac{WV}{WZ}=\frac{p}{q},
\]
where $p$ and $q$ are relatively prime positive integers, then $p+q=$

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