
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
Consider the function $g(x)$ defined for $-1 \leq x \leq 1$ by the formula 
$$g(x) = 1 - \sqrt{1 - (x-0.5)^2}.$$ 
Suppose a graph of $y = g(x)$ is drawn. If a graph of $x = g(y)$ is overlaid on this graph, two distinct regions may be formed. What are the areas of these regions, rounded to the nearest hundredth?

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