
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
Famous skater Tony Hawk rides a skateboard (segment $AB$) in a ramp, which is a semicircle with a diameter $PQ$. Point $M$ is the midpoint of the skateboard, and $C$ is the foot of the perpendicular dropped from point $A$ to the diameter $PQ$. What values can the angle $\angle ACM$ take if the angular measure of arc $AB$ is $24^{\circ}$?

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