
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
A zig-zag line starts at the point \( P \), at one end of the diameter \( PQ \) of a circle. Each of the angles between the zig-zag line and the diameter \( PQ \) is equal to \( \alpha \). After four peaks, the zig-zag line ends at the point \( Q \). What is the size of angle \( \alpha \)?
A \( 60^{\circ} \)
B \( 72^{\circ} \)
C \( 75^{\circ} \)
D \( 80^{\circ} \)
E \( 86^{\circ} \)

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