
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
Points  $X$  and  $Y$  are the midpoints of arcs  $AB$  and  $BC$  of the circumscribed circle of triangle  $ABC$ . Point  $T$  lies on side  $AC$ . It turned out that the bisectors of the angles  $ATB$  and  $BTC$  pass through points  $X$  and  $Y$  respectively. What angle  $B$  can be in  triangle  $ABC$ ?

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