
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 $ABCD$, where $AB$ is parallel to $CD$, the height from $B$ to $AD$ is 5 units, and the bases $AB$ and $CD$ have unknown equal lengths. If $AD = 20$ units and $BC = 12$ units, determine the perimeter and the area of trapezoid $ABCD$.

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