
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  $XYZ$  be a triangle with  $ \angle X = 60^\circ $  and  $ \angle Y = 45^\circ $ . A circle with center  $P$  passes through points  $A$  and  $B$  on side  $XY$ ,  $C$  and  $D$  on side  $YZ$ , and  $E$  and  $F$  on side  $ZX$ . Suppose  $AB=CD=EF$ . Find  $ \angle XPY $  in degrees.

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