
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 $ABCD$, the bases $AB$ and $CD$ are not parallel. Let $AB = 20$, $CD = 12$, and height from $B$ to $CD$ be $5$. The sides $AD$ and $BC$ are equal. Calculate the perimeter of trapezoid $ABCD$. [asy]
pen p = linetype("4 4");
draw((0,0)--(8,5)--(20,5)--(28,0)--cycle);
draw((8,0)--(8,5), p);
draw((7.5,0)--(7.5, .5)--(8,0.5));

label(scale(0.75)*"A", (0,0), W);
label(scale(0.75)*"B", (8,5), NW);
label(scale(0.75)*"C", (20, 5), NE);
label(scale(0.75)*"D", (28, 0), E);
label(scale(0.75)*"12", (14,5), N);
label(scale(0.75)*"20", (14,0), S);
label(scale(0.75)*"5", (8, 2.5), E);
[/asy]

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