
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
Point \( M \) is the midpoint of leg \( AB \) of the isosceles right triangle \( ABC \) with the right angle \( \angle B \). The angle bisector of \( \angle A \) intersects the circumcircle of the triangle at point \( L \). Point \( H \) is the foot of the perpendicular dropped from \( L \) to line \( AC \). Find the angle \( \angle AMH \).

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