
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
Point \( O \) is the center of the circumscribed circle of triangle \( ABC \). A point \( X \) is chosen on the circumscribed circle of triangle \( BOC \) outside of triangle \( ABC \). Points \( Y \) and \( Z \) are chosen on the rays \( XB \) and \( XC \) beyond points \( B \) and \( C \) respectively, such that \( XY = XZ \). The circumscribed circle of triangle \( ABY \) intersects side \( AC \) at point \( T \). Find the angle \( \angle YTZ \).

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