
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 square with side length 2 is rotated around one of its vertices by an angle of \(\beta\), where \(0^\circ < \beta < 90^\circ\) and \(\cos \beta = \frac{3}{5}\). Find the area of the shaded region that is common to both the original and the rotated square.

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