
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
Let $ABCD$ be a trapezoid, not necessarily isosceles, with $\overline{BC}\parallel \overline{AD}$ and $\angle A = \angle D = 90^\circ$. Points $X$ and $Y$ lie on diagonal $\overline{AC}$ with $X$ between $A$ and $Y$. Suppose $\angle AXD = 60^\circ$, $\angle BYC = 60^\circ$, $AX = 4$, $XY = 2$, and $YC = 1$. Calculate the area of trapezoid $ABCD.$
A) 12.5
B) 12.75
C) 13
D) 13.25
E) 14

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