
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
Let $g(x)$ be the function defined on $-2\le x\le 2$ by the formula $$g(x) = 2 - \sqrt{4-x^2}.$$ If a graph of $x = g(y)$ is overlaid on the graph of $y = g(x)$, then determine the area of the fully enclosed region.

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