
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 $WXYZ$, $M$ is a point on $WY$ such that $\angle WMN=90^{\circ}$. $UV$ is perpendicular to $WY$ with $WU=UM$, as shown. $MU$ intersects $NV$ at $R$. Point $T$ is on $YZ$ such that $WT$ passes through $R$. In $\triangle MRU$, $MU=18$, $RU=27$, and $MR=15$. Find $VY$.

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