
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 concentric circles have radii $b$ and $c$, with $b>c$. Let $\overline{OX}$ be a radius of the smaller circle, let $\overline{XZ}$ be tangent to the larger circle at $Z$, and let $\overline{OY}$ be the radius of the smaller circle that contains $Z$. Let $a=XZ$, $d=YZ$, and $e=XY$. What is the area of the annulus? Express your answer in terms of $\pi$ and at most one of the variables $a,b,c,d,e$.

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