
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
An $\textit{annulus}$ is formed between two concentric circles with radii $R$ and $r$ where $R>r$. Let $\overline{OP}$ be a radius of the larger circle, let $\overline{PQ}$ be tangent to the smaller circle at point $Q$, and let $\overline{OR}$ be the radius of the larger circle that contains $Q$. Let $x = PQ$, $y = QR$, and $z = PR$. Calculate the area of the annulus. Express your answer in terms of $\pi$ and at most one of the variables $x, R, r, y, z$.

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