
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
Circles $X$ and $Y$ each have a radius of 1, while circle $Z$ has a radius of 2. Circle $X$ and circle $Y$ share one point of tangency. Circle $Z$ is tangent to Circle $X$ at a point on the extension of the diameter of circle $X$ that starts at the point of tangency with circle $Y$. Find the area inside circle $Z$ but outside circle $X$ and circle $Y$.

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