
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 annulus is formed by two concentric circles with radii $r$ and $s$, where $r > s$. Let $\overline{OP}$ be a radius of the larger circle, let $\overline{PQ}$ be tangent to the smaller circle at $Q$, and let $\overline{OR}$ be the radius of the larger circle that contains $Q$. Let $x=PQ$, $u=QR$, and $v=PR$. Calculate the area of the annulus in terms of $\pi$ and at most one of the variables $x, r, s, u, v$.

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