
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
$EF \parallel AB$, hence, $\angle EFN = \angle BPF$ as corresponding angles. Similarly, $\angle ENF = \angle CKN$. Then $\angle CKN = \angle BPK = 180^\circ - \angle DKP = 180^\circ - 105^\circ = 75^\circ$. Therefore, $\angle BPK = 75^\circ$.

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