
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 parallelogram $ABCD$, it is known that $AB = 4$ and $AD = 6$. The bisector of angle $BAD$ intersects side $BC$ at point $M$, and $AM = 4\sqrt{3}$.

Find the area of quadrilateral $AMCD$.

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