
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 rectangle $WXYZ$, $P$ is a point on $WY$ such that $\angle WPZ=90^{\circ}$. $UV$ is perpendicular to $WY$ with $WU=UP$, as shown. $PZ$ intersects $UV$ at $Q$. Point $R$ is on $YZ$ such that $WR$ passes through $Q$. In $\triangle PQW$, $PW=15$, $WQ=20$ and $QP=25$. Find $VZ$. (Express your answer as a common fraction.)

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