
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 plane, five circles with radii $2,4,6,8,$ and $10$ are tangent to line $\ell$ at the same point $A,$ but they are arranged alternately on either side of $\ell$. Region $T$ consists of all the points that lie inside exactly three of the five circles. Calculate the maximum possible area of region $T$.
A) $28\pi$  
B) $32\pi$  
C) $56\pi$  
D) $64\pi$

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