
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 trapezoid $WXYZ$, the sides $WZ$ and $XY$ are parallel, and the lengths of $WX$ and $YZ$ are equal. Given that $WZ = 10$, $XY = 18$, and the height of the trapezoid (the perpendicular distance between the lines containing $WZ$ and $XY$) is 5, what is the perimeter of $WXYZ$?

[asy]
pen p = linetype("4 4");
draw((0,0)--(5,5)--(15,5)--(20,0)--cycle);
draw((5,0)--(5,5), p);
label(scale(0.75)*"W", (0,0), W);
label(scale(0.75)*"X", (5,5), NW);
label(scale(0.75)*"Y", (15,5), NE);
label(scale(0.75)*"Z", (20, 0), E);
label(scale(0.75)*"18", (10,5), N);
label(scale(0.75)*"10", (10,0), S);
label(scale(0.75)*"5", (5, 2.5), E);
[/asy]

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