
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
Rectangle $ABCD$ has $AB = 8$ and $BC = 4$. Point $M$ is chosen on side $AB$ such that $AM = 2MB$ and $\angle AMD = \angle CMD$. What is the degree measure of $\angle AMD$?
**A)** 40
**B)** 45
**C)** 50
**D)** 55
**E)** 60

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