
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
Peter drew a trapezoid $ABCD$ where base $AB$ was twice as long as base $CD$, and sides $AD$, $DC$, and $CB$ were congruent. Then, he completed a square sharing one side with the shorter base of the trapezoid. The new vertex of the square, which was closer to $B$ than $A$, was labeled $N$.

What could be the measure of angle $ABN$? Determine all possible values.

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