
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
Quadrilateral \(ABCD\) is inscribed in a circle. A perpendicular to side \(BC\), drawn through its midpoint \(M\), intersects side \(AB\) at point \(K\). A circle with diameter \(KC\) intersects segment \(CD\) at point \(P\) (where \(P \neq C\)). Find the angle between lines \(MP\) and \(AD\).

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