
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 
\[ g(x) = 1 - \sqrt{4 - x^2}. \]
Calculate the area of the fully enclosed region when the graph of \( y = g(x) \) is overlaid with the graph of \( x = g(y) \).

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