
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 a trapezoid, the smaller base is equal to 2, and the adjacent angles are each $135^{\circ}$. The angle between the diagonals, facing the base, is $150^{\circ}$. Find the area of the trapezoid.

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-0942.jpg?height=243&width=679&top_left_y=918&top_left_x=595)

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