
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 convex quadrilateral such that the triangle  $ABD$  is equilateral and the triangle  $BCD$  is isosceles, with  $\angle C = 90^o$ . If  $E$  is the midpoint of the side  $AD$ , determine the measure of the angle  $\angle CED$ .

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