
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
Given that the dihedral angle \( M-AB-N \) is a right dihedral angle, \( P \) is a point on the edge \( AB \). Lines \( PX \) and \( PY \) are in planes \( M \) and \( N \) respectively, and \(\angle XPB = \angle YPB = 45^\circ\). Find the measure of \(\angle XPY\).

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