
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
Given an isosceles triangle \(ABC\) with \(\angle A = 30^\circ\) and \(AB = AC\). Point \(D\) is the midpoint of \(BC\). Point \(P\) is chosen on segment \(AD\), and point \(Q\) is chosen on side \(AB\) such that \(PB = PQ\). What is the measure of angle \(PQC\)?

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