
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 a convex quadrilateral \(ABCD\), the lengths of the sides \(BC\) and \(AD\) are 2 and \(2 \sqrt{2}\) respectively. The distance between the midpoints of the diagonals \(BD\) and \(AC\) is 1. Find the angle between the lines \(BC\) and \(AD\).

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