
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  $ABCD$  with  $AD\parallel BC$ ,  $AB=6$ ,  $AD=9$ , and  $BD=12$ . If  $\angle ABD=\angle DCB$ , find the perimeter of the trapezoid.

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