
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 $WXYZ$ is inscribed in rectangle $EFGH$ such that vertices $W$, $X$, $Y$, and $Z$ are interior points on sides $\overline{EF}$, $\overline{FG}$, $\overline{GH}$, and $\overline{HE}$, respectively. It is given that $WE = 12$, $EX = 16$, $WY = 24$, and $XZ = 32$. Let $p/q$, in lowest terms, denote the perimeter of $EFGH$. Find $p+q$.

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