
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
On side \( AB \) of rectangle \( ABCD \), point \( M \) is chosen. A perpendicular to line \( CM \) is drawn through this point, which intersects side \( AD \) at point \( E \). Point \( P \) is the foot of the perpendicular dropped from point \( M \) to line \( CE \). Find the angle \( \angle APB \).

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