
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
Rhombus $ABCD$ is inscribed in rectangle $WXYZ$ such that vertices $A$, $B$, $C$, and $D$ are on sides $\overline{WX}$, $\overline{XY}$, $\overline{YZ}$, and $\overline{ZW}$, respectively. It is given that $WA=12$, $XB=9$, $BD=15$, and the diagonal $AC$ of rhombus equals side $XY$ of the rectangle. Calculate the perimeter of rectangle $WXYZ$.

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