
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 defined by two concentric circles with radii $R$ and $r$, where $R > r$. Let $\overline{OA}$ be a radius of the larger circle that terminates at point $A$ on the circumference. Let $\overline{AB}$ be a chord of the larger circle that is tangent to the smaller circle at point $P$. Let $\overline{OB}$ be another radius of the larger circle, and let the length of $\overline{AB}$ be $l$. Find the area of the annulus.

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