
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
On the hypotenuse \( AC \) of the right triangle \( ABC \), a point \( C_1 \) is marked such that \( BC = CC_1 \). Then, on the leg \( AB \), a point \( C_2 \) is marked such that \( AC_2 = AC_1 \); similarly, the point \( A_2 \) is determined. Find the angle \( AMC \), where \( M \) is the midpoint of the segment \( A_2C_2 \).

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