
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 point $P$ in the plane, where $P \in {(x,y) | (x - 2\cos{\alpha})^2 + (y - 2\sin{\alpha})^2 = 16, \alpha \in \mathbb{R}}$, the area of the shape formed by all such points $P$ in the plane is $\_\_\_\_\_\_$.

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