
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
The rectangle with vertices (0, 0), (0, 3), (2, 0), and (2, 3) is rotated clockwise through a right angle about the point (2, 0), then about (5, 0), then about (7, 0), and finally about (10, 0). The net effect is to translate it a distance of 10 along the x-axis. The point initially at (1, 1) traces out a curve. Find the area under this curve (in other words, the area of the region bounded by the curve, the x-axis, and the lines parallel to the y-axis through (1, 0) and (11, 0)).

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