
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
In a coordinate plane, consider a larger circle with radius $R$ and a smaller circle with radius $r$, where $R > r$. Both circles are concentric at the origin $(0,0)$. Let $\overline{OA}$ be the radius of the larger circle extending to point $A=(R,0)$. Draw a line from $A$ to a point $B$ on the $y-axis$ such that $B=(0,y)$ and line segment $\overline{AB}$ is perpendicular to the $y-axis$. Let the length of $AB$ equal $s$. Also assume that $R^2 - r^2 = s^2$. Find the area of the annulus formed between these two circles.

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