
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  $AB = CD$ ,  $\angle BCD = 2 \angle BAD$ ,  $\angle ABC = 2 \angle ADC$  and  $\angle BAD  \neq \angle ADC$ . Determine the measure of the angle between the diagonals  $AC$  and  $BD$ .

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