
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
A rectangle $ABCD$ has a rhombus $WXYZ$ inscribed such that vertices $W$, $X$, $Y$, and $Z$ are on sides $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, and $\overline{DA}$, respectively. Given that $WA=10$, $BX=25$, $WY=35$, and $XZ=50$. Determine the perimeter of rectangle $ABCD$ in its simplest form.

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