
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
The "heart" shown in the diagram is formed from an equilateral triangle \(A B C\) and two congruent semicircles on \(A B\). The two semicircles meet at the point \(P\). The point \(O\) is the center of one of the semicircles. On the semicircle with center \(O\), lies a point \(X\). The lines \(X O\) and \(X P\) are extended to meet \(A C\) at \(Y\) and \(Z\) respectively. The lines \(X Y\) and \(X Z\) are of equal length. What is \(\angle Z X Y\)?

A) \(20^{\circ}\)

B) \(25^{\circ}\)

C) \(30^{\circ}\)

D) \(40^{\circ}\)

E) \(45^{\circ}\)

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