
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 rectangle  $ABCD$ ,  $AB = 2BC$ . An equilateral triangle  $ABE$  is constructed on the side  $AB$  of the rectangle so that its sides  $AE$  and  $BE$  intersect the segment  $CD$ . Point  $M$  is the midpoint of  $BE$ . Find the  $\angle MCD$ .

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