
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
The height of trapezoid $ABCD$ is 5, and the bases $BC$ and $AD$ are 3 and 5 respectively. Point $E$ is on side $BC$ such that $BE=2$. Point $F$ is the midpoint of side $CD$, and $M$ is the intersection point of segments $AE$ and $BF$. Find the area of quadrilateral $AMFD$.

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