
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 $XYZW$, point $M$ is on $YZ$ so that $\angle XMW=90^{\circ}$. $UV$ is perpendicular to $YZ$ with $YM=MV$, as shown. $MW$ intersects $UV$ at point $N$. Point $S$ is on $ZW$ such that $SX$ passes through $N$. In $\triangle MNX$, $MX=24$, $XN=32$ and $MN=40$. Find $VW$.

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