
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
Cyclic quadrilateral  $ABCD$  satisfies  $\angle ABD = 70^\circ$ ,  $\angle ADB=50^\circ$ , and  $BC=CD$ .  Suppose  $AB$  intersects  $CD$  at point  $P$ , while  $AD$  intersects  $BC$  at point  $Q$ .  Compute  $\angle APQ-\angle AQP$ .

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