
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 the hypotenuse \( AC \) of right triangle \( ABC \). Points \( P \) and \( Q \) on lines \( AB \) and \( BC \) respectively are such that \( AP = PM \) and \( CQ = QM \). Find the measure of angle \( \angle PQM \) if \( \angle BAC = 17^{\circ} \).

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