
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
Let  $ABC$  be an acute-angled scalene triangle and  $T$  be a point inside it such that  $\angle ATB  = \angle BTC = 120^o$ . A circle centered at point  $E$  passes through the midpoints of the sides of  $ABC$ . For  $B, T, E$  collinear, find angle  $ABC$ .

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