
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
Calculate the area of the shape bounded by the lines given by the equations:

$$
\begin{aligned}
& \left\{\begin{array}{l}
x=t-\sin t \\
y=1-\cos t
\end{array}\right. \\
& y=1 \quad (0<x<2\pi, \, y \geq 1)
\end{aligned}
$$

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