
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
Equilateral triangle  $ABC$  has point  $P$  inside and point  $Q$  on side  $BC$ , satisfying  $PB = PQ = QC$  and  $\angle PBC = 20^\circ$ .
Find the measure of  $\angle AQP$ .

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