
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 the trapezoid \( ABCD \) with bases \( AD \) and \( BC \), the side \( AB \) is equal to 2. The angle bisector of \( \angle BAD \) intersects the line \( BC \) at point \( E \). A circle is inscribed in triangle \( ABE \), touching side \( AB \) at point \( M \) and side \( BE \) at point \( H \). Given that \( MH = 1 \), find the angle \( \angle BAD \).

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