
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
In the diagram, square $ABCD$ has sides of length $6$. Triangle $ABE$ is an isosceles triangle with $AB = AE$ and $\angle ABE = 75^\circ$. Line segments $BE$ and $AC$ intersect at $P$. Point $Q$ is on $BC$ such that $PQ$ is perpendicular to $BC$. Determine the measure of angle $BPC$.

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