
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
Quadrilateral $ABCD$ satisfies $AB = 20, \angle{A} = 45^\circ,$ and $\overline{AB} \parallel \overline{CD}.$ The side lengths of $ABCD$ form an arithmetic progression, with $\overline{AB}$ as the longest side. Determine the possible lengths of side DC.
**A)** 12 
**B)** 14 
**C)** 16 
**D)** 18

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