
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
 $M$  is the midpoint of the side  $AB$  in an equilateral triangle  $\triangle ABC.$  The point  $D$  on the side  $BC$  is such that  $BD : DC = 3 : 1.$  On the line passing through  $C$  and parallel to  $MD$  there is a point  $T$  inside the triangle  $\triangle ABC$  such that  $\angle CTA = 150.$  Find the  $\angle MT D.$ *(K. Ivanov )*

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