
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
Let  $ABCD$  be a rectangle. Circles with diameters  $AB$  and  $CD$  meet at points  $P$  and  $Q$  inside the rectangle such that  $P$  is closer to segment  $BC$  than  $Q$ . Let  $M$  and  $N$  be the midpoints of segments  $AB$  and  $CD$ . If  $\angle MPN = 40^\circ$ , find the degree measure of  $\angle BPC$ .

*Ray Li.*

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