
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
A point \( M \) is marked on the circumcircle of square \( A B C D \) such that \( \angle M A B = 18^\circ \). The segment \( M D \) intersects the diagonal \( A C \) at point \( Q \).

What values can the angle \( \angle A Q D \) take? Express the answer in degrees and list all possible options.

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