
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
Four congruent circles with centers $P$, $Q$, $R$, and $S$ are arranged inside an extended rectangle $ABCD$ such that $P$ and $Q$ are inside, and $R$ and $S$ are placed symmetrically about $CD$ outside but still tangent to side $CD$. Each circle has a radius of $2$. The circle centered at $Q$ passes through point $P$, and similarly, $S$ through $R$. Calculate the total length of side $AB$ of the rectangle.
A) 4
B) 8
C) 12
D) 16
E) 20

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