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

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