
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
In the triangle  $ABC$  it is known that $\angle A = 75^o, \angle C = 45^o$ . On the ray  $BC$  beyond the point  $C$  the point  $T$  is taken so that  $BC = CT$ . Let  $M$  be the midpoint of the segment  $AT$ . Find the measure of the  $\angle BMC$ .

(Anton Trygub)

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