
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 $f(x)$ be the function defined on $0\le x\le 1$ by the formula $$f(x)=1-\sqrt{1-x^2}.$$ Reflect the graph of $y=f(x)$ about the line $y=1$ to get a new function $g(x)$. On the same axes, plot $x = g(y)$. Calculate the area of the fully enclosed region formed by the curves of $y = f(x)$ and $x = g(y)$.

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