
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 $-1\le x\le 1$ by the formula $$g(x) = 1 - \sqrt{1 - (x-1)^2}.$$ This is a graph of $y=g(x)$. If a graph of $x=g(y)$ is overlaid on the graph above, then one fully enclosed region is formed by the two graphs. What is the area of that region, rounded to the nearest hundredth?

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