
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
Consider three concentric circles with radii $r$, $s$, and $t$, where $r > s > t$. Let $\overline{OV}$ be a radius of the largest circle, and $\overline{VW}$ be tangent to the middle circle at $W$ with length $p$. Also, let $\overline{UW}$ be tangential to the smallest circle at $W$, where $\overline{OU}$ is the radius of the middle circle that contains $W$. Let $q = UW$ and $l = OV$. Calculate the area of the region between the largest and smallest circle.

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