
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
Given a $2 \times 3$ rectangle with vertices at $(0,0), (2,0), (0,3), (2,3)$, rotate it clockwise $90^{\circ}$ around the point $(2,0)$, then another $90^{\circ}$ clockwise around the point $(5,0)$, followed by another $90^{\circ}$ clockwise around the point $(7,0)$, and finally rotate it another $90^{\circ}$ clockwise around the point $(10,0)$. This brings the rectangle back to its original position on the $x$-axis. Initially, a point on the rectangle at $(1,1)$ traces a curve through these rotations. Find the area of the region below this curve and above the $x$-axis.

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