
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 $MNPQ$, $R$ is a point on $NQ$ such that $\angle MRS=90^{\circ}$. $UV$ is perpendicular to $NQ$ with $NR=RU$, as shown. $RS$ intersects $UV$ at $T$. Point $W$ is on $PQ$ such that $WM$ passes through $T$. In $\triangle RTM$, $RM=15$, $MT=20$, and $RT=25$. Find $VS$. (Express your answer as a common fraction.)

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