
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 right trapezoid \(ABCD\) is given, with a right angle at vertex \(B\) and parallel sides \(AB\) and \(CD\). The diagonals of the trapezoid are perpendicular to each other and have lengths \(|AC| = 12 \, \text{cm}\) and \(|BD| = 9 \, \text{cm}\). Calculate the perimeter and the area of this trapezoid.

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