
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
The distance between the midpoints of the sides \(AB\) and \(CD\) of a convex quadrilateral \(ABCD\) is equal to the distance between the midpoints of its diagonals. Find the angle formed by the lines \(AD\) and \(BC\) at their intersection. Justify your answer.

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