
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 convex quadrilateral  $ABCD$ ,  $\angle BAD = \angle BCD = 90^o$ , and  $BC = CD$ . Let  $E$  be the intersection of diagonals  $\overline{AC}$  and  $\overline{BD}$ . Given that  $\angle AED = 123^o$ , find the degree measure of  $\angle ABD$ .

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