
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 \( ABCD \), two equal circles are inscribed such that they touch each other. The center of the first circle lies on the segment connecting vertex \( D \) and the midpoint \( E \) of side \( AB \), while the center of the second circle lies on segment \( CE \). The first circle touches sides \( AB \), \( AD \), and \( CD \), and the second circle touches sides \( AB \), \( BC \), and \( CD \). Find the sine of the angle between the diagonals of quadrilateral \( ABCD \).

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