
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 an isosceles trapezoid  $ABCD$ , the base  $AB$  is twice as large as the base  $CD$ . Point  $M$  is the midpoint of  $AB$ . It is known that the center of the circle inscribed in the triangle  $MCB$  lies on the circle circumscribed around the triangle  $MDC$ . Find the angle  $\angle MBC$ .
![Image](https://cdn.artofproblemsolving.com/attachments/8/a/7af6a1d32c4e2affa49cb3eed9c10ba1e7ab71.png)

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