
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
Let  $ABCD$  be a quadrilateral with  $AD = 20$  and  $BC = 13$ .  The area of  $\triangle ABC$  is  $338$  and the area of  $\triangle DBC$  is  $212$ .  Compute the smallest possible perimeter of  $ABCD$ .

*Proposed by Evan Chen*

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