
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
Let \( ABC \) be a triangle and \( \omega \) be its circumcircle. The point \( M \) is the midpoint of arc \( BC \) not containing \( A \) on \( \omega \) and \( D \) is chosen so that \( DM \) is tangent to \( \omega \) and is on the same side of \( AM \) as \( C \). It is given that \( AM = AC \) and \( \angle DMC = 38^\circ \). Find the measure of angle \( \angle ACB \).

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