
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 the region between two concentric circles. The outer and inner circles have radii $R$ and $r$ respectively, with $R>r$. Let $\overline{OA}$ be a radius of the larger circle, and $\overline{AP}$ be part of a chord of the larger circle extended to touch the smaller circle tangentially at point $P$. Let $\overline{OP}$, which passes through $P$, intersect the larger circle at point $B$ so that $P$ is between $O$ and $B$. If $l = AP$ (the length of the tangent from $A$ to the smaller circle at $P$) and $m = PB$ (the length on the larger circle's radius beyond $P$), find the area of the annulus in terms of $\pi$ and $l$.

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