
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
A trapezoid $ABCD$, where side $AB$ is parallel to side $CD$, is divided by its diagonals, which intersect at point $M$, into four parts. Determine its area, given that the triangle $AMD$ has an area of $8 \ \mathrm{cm}^{2}$ and the triangle $DCM$ has an area of $4 \ \mathrm{cm}^{2}$.

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