
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 rectangle with side lengths 2 (length) and 1 (width) is rotated around one vertex by an angle of $\beta,$ where $0^\circ < \beta < 90^\circ$ and $\sin \beta = \frac{3}{5}.$ Calculate the area of the region common to both the original and the rotated rectangle.

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